Showing 1–50 of 87 results for author: Mohseni, M

Impacts of Decoder Latency on Utility-Scale Quantum Computer Architectures

Authors: Abdullah Khalid, Allyson Silva, Gebremedhin A. Dagnew, Tom Dvir, Oded Wertheim, Motty Gruda, Xiangzhou Kong, Mia Kramer, Zak Webb, Artur Scherer, Masoud Mohseni, Yonatan Cohen, Pooya Ronagh

Abstract: The speed of a fault-tolerant quantum computer is dictated by the reaction time of its classical electronics, that is, the total time required by decoders and controllers to determine the outcome of a logical measurement and execute subsequent conditional logical operations. Despite its importance, the reaction time and its impact on the design of the logical microarchitecture of a quantum compute… ▽ More The speed of a fault-tolerant quantum computer is dictated by the reaction time of its classical electronics, that is, the total time required by decoders and controllers to determine the outcome of a logical measurement and execute subsequent conditional logical operations. Despite its importance, the reaction time and its impact on the design of the logical microarchitecture of a quantum computer are not well understood. In this work, we build, for a surface code based architecture, a model for the reaction time in which the decoder latency is based on parallel space- and time-window decoding methods, and communication latencies are drawn from our envisioned quantum execution environment comprising a high-speed network of quantum processing units, controllers, decoders, and high-performance computing nodes. We use this model to estimate the increase in the logical error rate of magic state injections as a function of the reaction time. Next, we show how the logical microarchitecture can be optimized with respect to the reaction time, and then present detailed full-system quantum and classical resource estimates for executing utility-scale quantum circuits based on realistic hardware noise parameters and state-of-the-art decoding times. For circuits with $10^{6}$--$10^{11}$ $T$ gates involving 200--2000 logical qubits, under a $Λ=9.3$ hardware model representative of a realistic target for superconducting quantum processors operating at a 2.86 MHz stabilization frequency, we show that even decoding at a sub-microsecond per stabilization round speed introduces substantial resource overheads: approximately 100k--250k additional physical qubits for correction qubit storage in the magic state factory; 300k--1.75M extra physical qubits in the core processor due to the code distance increase of $d$ to $d+4$ for extra memory protection; and a longer runtime by roughly a factor of 100. △ Less

Submitted 13 November, 2025; originally announced November 2025.

Comments: 23 pages, 7 figures

A Full Stack Framework for High Performance Quantum-Classical Computing

Authors: Xin Zhan, K. Grace Johnson, Aniello Esposito, Barbara Chapman, Marco Fiorentino, Kirk M. Bresniker, Raymond G. Beausoleil, Masoud Mohseni

Abstract: To address the growing needs for scalable High Performance Computing (HPC) and Quantum Computing (QC) integration, we present our HPC-QC full stack framework and its hybrid workload development capability with modular hardware/device-agnostic software integration approach. The latest development in extensible interfaces for quantum programming, dispatching, and compilation within existing mature H… ▽ More To address the growing needs for scalable High Performance Computing (HPC) and Quantum Computing (QC) integration, we present our HPC-QC full stack framework and its hybrid workload development capability with modular hardware/device-agnostic software integration approach. The latest development in extensible interfaces for quantum programming, dispatching, and compilation within existing mature HPC programming environment are demonstrated. Our HPC-QC full stack enables high-level, portable invocation of quantum kernels from commercial quantum SDKs within HPC meta-program in compiled languages (C/C++ and Fortran) as well as Python through a quantum programming interface library extension. An adaptive circuit knitting hypervisor is being developed to partition large quantum circuits into sub-circuits that fit on smaller noisy quantum devices and classical simulators. At the lower-level, we leverage Cray LLVM-based compilation framework to transform and consume LLVM IR and Quantum IR (QIR) from commercial quantum software frontends in a retargetable fashion to different hardware architectures. Several hybrid HPC-QC multi-node multi-CPU and GPU workloads (including solving linear system of equations, quantum optimization, and simulating quantum phase transitions) have been demonstrated on HPE EX supercomputers to illustrate functionality and execution viability for all three components developed so far. This work provides the framework for a unified quantum-classical programming environment built upon classical HPC software stack (compilers, libraries, parallel runtime and process scheduling). △ Less

Submitted 22 October, 2025; originally announced October 2025.

Comments: 9 pages, 8 figures, presented at Cray User Group Meeting 2025, May 04-09, 2025, New York, NY

ACM Class: D.2.6

Pushing the Boundary of Quantum Advantage in Hard Combinatorial Optimization with Probabilistic Computers

Authors: Shuvro Chowdhury, Navid Anjum Aadit, Andrea Grimaldi, Eleonora Raimondo, Atharva Raut, P. Aaron Lott, Johan H. Mentink, Marek M. Rams, Federico Ricci-Tersenghi, Massimo Chiappini, Luke S. Theogarajan, Tathagata Srimani, Giovanni Finocchio, Masoud Mohseni, Kerem Y. Camsari

Abstract: Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers), when co-designed with hardware to implement powerful Monte Carlo algorithms, provide a compelling and scalable classical pathway for solving ha… ▽ More Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers), when co-designed with hardware to implement powerful Monte Carlo algorithms, provide a compelling and scalable classical pathway for solving hard optimization problems. We focus on two key algorithms applied to 3D spin glasses: discrete-time simulated quantum annealing (DT-SQA) and adaptive parallel tempering (APT). We benchmark these methods against the performance of a leading quantum annealer on the same problem instances. For DT-SQA, we find that increasing the number of replicas improves residual energy scaling, in line with expectations from extreme value theory. We then show that APT, when supported by non-local isoenergetic cluster moves, exhibits a more favorable scaling and ultimately outperforms DT-SQA. We demonstrate these algorithms are readily implementable in modern hardware, projecting that custom Field Programmable Gate Arrays (FPGA) or specialized chips can leverage massive parallelism to accelerate these algorithms by orders of magnitude while drastically improving energy efficiency. Our results establish a new, rigorous classical baseline, clarifying the landscape for assessing a practical quantum advantage and presenting p-computers as a scalable platform for real-world optimization challenges. △ Less

Submitted 27 July, 2025; v1 submitted 13 March, 2025; originally announced March 2025.

Comments: Codes are openly available at https://github.com/OPUSLab/3DSpinGlassWithPbits.git

Journal ref: Nature Communications, 2025

Limitations of tensor network approaches for optimization and sampling: A comparison to quantum and classical Ising machines

Authors: Anna Maria Dziubyna, Tomasz Śmierzchalski, Bartłomiej Gardas, Marek M. Rams, Masoud Mohseni

Abstract: Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN) based algorithm to reveal the low-energy spectrum of Ising spin-glass systems with interaction graphs relevant to present-day quantum annealers. Our deterministic a… ▽ More Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN) based algorithm to reveal the low-energy spectrum of Ising spin-glass systems with interaction graphs relevant to present-day quantum annealers. Our deterministic approach combines a branch-and-bound search strategy with an approximate calculation of marginals via TN contractions. Its application to quasi-two-dimensional lattices with large unit cells of up to 24 spins, realized in current quantum annealing processors, requires a dedicated approach that utilizes sparse structures in the TN representation and GPU hardware acceleration. We benchmark our approach on random problems defined on Pegasus and Zephyr graphs with up to a few thousand spins, comparing it against the D-Wave Advantage quantum annealer and Simulated Bifurcation algorithm. Apart from the quality of the best solutions, we compare the diversity of low-energy states sampled by all the solvers. For the biggest considered i.i.d. problems with over 5000 spins, the state-of-the-art TN approach leads to solutions that are $0.1\%$ to $1\%$ worse than the best solutions obtained by Ising machines while being two orders of magnitude slower. We attribute those results to approximate contraction failures. For embedded tile planting instances, our approach gets to approximately $0.1\%$ from the planted ground state, a factor of $3$ better than the Ising solvers. While all three methods can output diverse low-energy solutions, e.g., differing by at least a quarter of spins with energy error below $1\%$, our deterministic branch-and-bound approach finds sets of a few such states at most. On the other hand, both Ising machines prove capable of sampling sets of thousands of such solutions. △ Less

Submitted 16 June, 2025; v1 submitted 25 November, 2024; originally announced November 2024.

Comments: 16+7 pages, 12+7 figures; close to published version

Journal ref: Phys. Rev. Applied 23, 054049 (2025)

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

Authors: Masoud Mohseni, Artur Scherer, K. Grace Johnson, Oded Wertheim, Matthew Otten, Navid Anjum Aadit, Yuri Alexeev, Kirk M. Bresniker, Kerem Y. Camsari, Barbara Chapman, Soumitra Chatterjee, Gebremedhin A. Dagnew, Aniello Esposito, Farah Fahim, Marco Fiorentino, Archit Gajjar, Abdullah Khalid, Xiangzhou Kong, Bohdan Kulchytskyy, Elica Kyoseva, Ruoyu Li, P. Aaron Lott, Igor L. Markov, Robert F. McDermott, Giacomo Pedretti , et al. (16 additional authors not shown)

Abstract: In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits and proof-of-principle error-correction on a single logical qubit. Nevertheless, despite significant progress and excitement, the path toward a ful… ▽ More In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits and proof-of-principle error-correction on a single logical qubit. Nevertheless, despite significant progress and excitement, the path toward a full-stack scalable technology is largely unknown. There are significant outstanding quantum hardware, fabrication, software architecture, and algorithmic challenges that are either unresolved or overlooked. These issues could seriously undermine the arrival of utility-scale quantum computers for the foreseeable future. Here, we provide a comprehensive review of these scaling challenges. We show how the road to scaling could be paved by adopting existing semiconductor technology to build much higher-quality qubits, employing system engineering approaches, and performing distributed quantum computation within heterogeneous high-performance computing infrastructures. These opportunities for research and development could unlock certain promising applications, in particular, efficient quantum simulation/learning of quantum data generated by natural or engineered quantum systems. To estimate the true cost of such promises, we provide a detailed resource and sensitivity analysis for classically hard quantum chemistry calculations on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. Furthermore, we argue that, to tackle industry-scale classical optimization and machine learning problems in a cost-effective manner, heterogeneous quantum-probabilistic computing with custom-designed accelerators should be considered as a complementary path toward scalability. △ Less

Submitted 31 January, 2025; v1 submitted 15 November, 2024; originally announced November 2024.

Comments: 76 pages, 46 figures. General revision, added figures, added references, added appendices

Designing Majorana Quasiparticles in InAsP Quantum Dots in InP Nanowires with Variational Quantum Eigenvalue Solver

Authors: Mahan Mohseni, Iann Cunha, Daniel Miravet, Alina Wania Rodrigues, Hassan Allami, Ibsal Assi, Marek Korkusinski, Pawel Hawrylak

Abstract: This work presents steps toward the design of Majorana zero modes (MZM) in InAsP quantum dots (QD) embedded in an InP semiconducting nanowire in contact with a p-type superconductor described by the Kitaev Hamiltonian. The single particle spectrum is obtained from million atom atomistic calculations with QNANO and many-electron spectra using exact diagonalization (ED) and the hybrid Variational Qu… ▽ More This work presents steps toward the design of Majorana zero modes (MZM) in InAsP quantum dots (QD) embedded in an InP semiconducting nanowire in contact with a p-type superconductor described by the Kitaev Hamiltonian. The single particle spectrum is obtained from million atom atomistic calculations with QNANO and many-electron spectra using exact diagonalization (ED) and the hybrid Variational Quantum Eigensolver (VQE) method. A variational ansatz is constructed to capture the ground state of the system by utilizing a generalized form of the analytical solution for a particular set of parameters. By systematically deviating from the analytically solvable regime while maintaining the system in the topological phase (TP), the effectiveness of the variational function in reproducing the correct ground state and topological properties of the system is evaluated. This is done through a quantum algorithm for a many-body state containing MZM. The results are compared with exact solution in topological phase and demonstrate the capability of VQE, along with classical simulations, to accurately model the many-body spectra in topologically nontrivial state. △ Less

Submitted 6 January, 2025; v1 submitted 29 October, 2024; originally announced October 2024.

Magneto-optical properties of Group-IV--vacancy centers in diamond upon hydrostatic pressure

Authors: Meysam Mohseni, Lukas Razinkovas, Vytautas Žalandauskas, Gergő Thiering, Adam Gali

Abstract: In recent years, the negatively charged group-IV--vacancy defects in diamond, labeled as G4V(-) or G4V centers, have attracted significant attention in quantum information processing. In this study, we investigate the magneto-optical properties of G4V centers under high compressive hydrostatic pressures up to 180 GPa. The spin-orbit splitting of the electronic ground and excited states, as well as… ▽ More In recent years, the negatively charged group-IV--vacancy defects in diamond, labeled as G4V(-) or G4V centers, have attracted significant attention in quantum information processing. In this study, we investigate the magneto-optical properties of G4V centers under high compressive hydrostatic pressures up to 180 GPa. The spin-orbit splitting of the electronic ground and excited states, as well as the hyperfine tensors, are calculated using plane-wave supercell density functional theory, providing distinctive fingerprints that uniquely characterize these defects. To this end, we develop a theory for calculating the hyperfine tensors when the electronic states are subject to the Jahn--Teller effect. We find that the zero-phonon-line energy increases with hydrostatic pressure, with the deformation potential increasing from SiV(-) to PbV(-). On the other hand, our calculated photoionization threshold energies indicate that PbV(-)-based quantum sensors can operate only up to 32 GPa, whereas SnV(-), GeV(-), and SiV(-) remain photostable up to 180 GPa. We also find that the spin-orbit splitting increases in both the electronic ground and excited states with increasing pressure. The optical transitions associated with the hyperfine fine structure of the dopant atoms are interpreted using our theoretical framework, which reproduces existing experimental data at zero strain. We show that the hyperfine levels are weakly dependent on magnetic field, and increasing pressure leads to optical transitions at longer wavelengths. Finally, we estimate the spin coherence times of the G4V centers under increasing hydrostatic pressure across different temperature regimes. △ Less

Submitted 1 October, 2025; v1 submitted 19 August, 2024; originally announced August 2024.

Comments: 23 pages, 8 figures, 12 tables

Journal ref: Phys. Rev. B 112, 155201 (2025)

The positively charged carbon vacancy defect as a near-infrared emitter in 4H-SiC

Authors: Meysam Mohseni, Péter Udvarhelyi, Gergő Thiering, Adam Gali

Abstract: Certain intrinsic point defects in silicon carbide are promising quantum systems with efficient spin-photon interface. Despite carbon vacancy in silicon carbide is an elementary and relatively abundant intrinsic defect, no optical signal has been reported associated with it. Here, we revisit the positively charged carbon vacancy defects in the 4H polytype of silicon carbide (4H-SiC) by means of \t… ▽ More Certain intrinsic point defects in silicon carbide are promising quantum systems with efficient spin-photon interface. Despite carbon vacancy in silicon carbide is an elementary and relatively abundant intrinsic defect, no optical signal has been reported associated with it. Here, we revisit the positively charged carbon vacancy defects in the 4H polytype of silicon carbide (4H-SiC) by means of \textit{ab initio} calculations. We find that the excited state is optically active for the so-called h-site configuration of carbon vacancy in 4H-SiC, with zero-phonon line at $0.65~\mathrm{eV}$. We propose this defect as an exotic paramagnetic near-infrared emitter in the IR-B region. △ Less

Submitted 27 May, 2023; originally announced May 2023.

Comments: 8 pages, 5 figures

Purification-based quantum error mitigation of pair-correlated electron simulations

Authors: T. E. O'Brien, G. Anselmetti, F. Gkritsis, V. E. Elfving, S. Polla, W. J. Huggins, O. Oumarou, K. Kechedzhi, D. Abanin, R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, K. Anderson, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, D. Bacon, J. C. Bardin, A. Bengtsson, S. Boixo, G. Bortoli, A. Bourassa , et al. (151 additional authors not shown)

Abstract: An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a ful… ▽ More An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), on up to $20$ qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations. △ Less

Submitted 19 October, 2022; originally announced October 2022.

Comments: 10 pages, 13 page supplementary material, 12 figures. Experimental data available at https://doi.org/10.5281/zenodo.7225821

Journal ref: Nat. Phys. (2023)

Non-Abelian braiding of graph vertices in a superconducting processor

Authors: Trond I. Andersen, Yuri D. Lensky, Kostyantyn Kechedzhi, Ilya Drozdov, Andreas Bengtsson, Sabrina Hong, Alexis Morvan, Xiao Mi, Alex Opremcak, Rajeev Acharya, Richard Allen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley , et al. (144 additional authors not shown)

Abstract: Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotatio… ▽ More Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing. △ Less

Submitted 31 May, 2023; v1 submitted 18 October, 2022; originally announced October 2022.

Information-theoretic Hardness of Out-of-time-order Correlators

Authors: Jordan Cotler, Thomas Schuster, Masoud Mohseni

Abstract: We establish that there are properties of quantum many-body dynamics which are efficiently learnable if we are given access to out-of-time-order correlators (OTOCs), but which require exponentially many operations in the system size if we can only measure time-ordered correlators. This implies that any experimental protocol which reconstructs OTOCs solely from time-ordered correlators must be, in… ▽ More We establish that there are properties of quantum many-body dynamics which are efficiently learnable if we are given access to out-of-time-order correlators (OTOCs), but which require exponentially many operations in the system size if we can only measure time-ordered correlators. This implies that any experimental protocol which reconstructs OTOCs solely from time-ordered correlators must be, in certain cases, exponentially inefficient. Our proofs leverage and generalize recent techniques in quantum learning theory. Along the way, we elucidate a general definition of time-ordered versus out-of-time-order experimental measurement protocols, which can be considered as classes of adaptive quantum learning algorithms. Moreover, our results provide a theoretical foundation for novel applications of OTOCs in quantum simulations. △ Less

Submitted 3 August, 2022; originally announced August 2022.

Comments: 5+13 pages, 2 figures and many diagrams

Learning quantum systems via out-of-time-order correlators

Authors: Thomas Schuster, Murphy Niu, Jordan Cotler, Thomas O'Brien, Jarrod R. McClean, Masoud Mohseni

Abstract: Learning the properties of dynamical quantum systems underlies applications ranging from nuclear magnetic resonance spectroscopy to quantum device characterization. A central challenge in this pursuit is the learning of strongly-interacting systems, where conventional observables decay quickly in time and space, limiting the information that can be learned from their measurement. In this work, we… ▽ More Learning the properties of dynamical quantum systems underlies applications ranging from nuclear magnetic resonance spectroscopy to quantum device characterization. A central challenge in this pursuit is the learning of strongly-interacting systems, where conventional observables decay quickly in time and space, limiting the information that can be learned from their measurement. In this work, we introduce a new class of observables into the context of quantum learning -- the out-of-time-order correlator -- which we show can substantially improve the learnability of strongly-interacting systems by virtue of displaying informative physics at large times and distances. We identify two general scenarios in which out-of-time-order correlators provide a significant advantage for learning tasks in locally-interacting systems: (i) when experimental access to the system is spatially-restricted, for example via a single "probe" degree of freedom, and (ii) when one desires to characterize weak interactions whose strength is much less than the typical interaction strength. We numerically characterize these advantages across a variety of learning problems, and find that they are robust to both read-out error and decoherence. Finally, we introduce a binary classification task that can be accomplished in constant time with out-of-time-order measurements. In a companion paper, we prove that this task is exponentially hard with any adaptive learning protocol that only involves time-ordered operations. △ Less

Submitted 3 August, 2022; originally announced August 2022.

Comments: 18 pages, 8 figures

Suppressing quantum errors by scaling a surface code logical qubit

Authors: Rajeev Acharya, Igor Aleiner, Richard Allen, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell , et al. (132 additional authors not shown)

Abstract: Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number… ▽ More Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation. △ Less

Submitted 20 July, 2022; v1 submitted 13 July, 2022; originally announced July 2022.

Comments: Main text: 6 pages, 4 figures. v2: Update author list, references, Fig. S12, Table IV

Journal ref: Nature 614 (2023) 678-681

Formation of robust bound states of interacting microwave photons

Authors: Alexis Morvan, Trond I. Andersen, Xiao Mi, Charles Neill, Andre Petukhov, Kostyantyn Kechedzhi, Dmitry Abanin, Rajeev Acharya, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger , et al. (125 additional authors not shown)

Abstract: Systems of correlated particles appear in many fields of science and represent some of the most intractable puzzles in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the 3-body problem and acceptable theory for strongly cor… ▽ More Systems of correlated particles appear in many fields of science and represent some of the most intractable puzzles in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the 3-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multi-particle bound states. In a ring of 24 superconducting qubits, we develop a high fidelity parameterizable fSim gate that we use to implement the periodic quantum circuit of the spin-1/2 XXZ model, an archetypal model of interaction. By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons. We devise a phase sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the common wisdom that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit. △ Less

Submitted 21 December, 2022; v1 submitted 10 June, 2022; originally announced June 2022.

Comments: 7 pages + 15 pages supplements

Journal ref: Nature 612, 240-245 (2022)

Noise-resilient Edge Modes on a Chain of Superconducting Qubits

Authors: Xiao Mi, Michael Sonner, Murphy Yuezhen Niu, Kenneth W. Lee, Brooks Foxen, Rajeev Acharya, Igor Aleiner, Trond I. Andersen, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Gina Bortoli, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell , et al. (103 additional authors not shown)

Abstract: Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $\mathbb{Z}_2$ parity symmetry. Remarkably, we find that any multi-qub… ▽ More Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $\mathbb{Z}_2$ parity symmetry. Remarkably, we find that any multi-qubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment. △ Less

Submitted 8 December, 2022; v1 submitted 24 April, 2022; originally announced April 2022.

Journal ref: Science 378, 785 (2022)

Quantum advantage in learning from experiments

Authors: Hsin-Yuan Huang, Michael Broughton, Jordan Cotler, Sitan Chen, Jerry Li, Masoud Mohseni, Hartmut Neven, Ryan Babbush, Richard Kueng, John Preskill, Jarrod R. McClean

Abstract: Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes… ▽ More Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature. △ Less

Submitted 1 December, 2021; originally announced December 2021.

Comments: 6 pages, 17 figures + 46 page appendix; open-source code available at https://github.com/quantumlib/ReCirq/tree/master/recirq/qml_lfe

Report number: Science 376, 1182--1186 (2022)

Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization

Authors: Masoud Mohseni, Daniel Eppens, Johan Strumpfer, Raffaele Marino, Vasil Denchev, Alan K. Ho, Sergei V. Isakov, Sergio Boixo, Federico Ricci-Tersenghi, Hartmut Neven

Abstract: Optimizing highly complex cost/energy functions over discrete variables is at the heart of many open problems across different scientific disciplines and industries. A major obstacle is the emergence of many-body effects among certain subsets of variables in hard instances leading to critical slowing down or collective freezing for known stochastic local search strategies. An exponential computati… ▽ More Optimizing highly complex cost/energy functions over discrete variables is at the heart of many open problems across different scientific disciplines and industries. A major obstacle is the emergence of many-body effects among certain subsets of variables in hard instances leading to critical slowing down or collective freezing for known stochastic local search strategies. An exponential computational effort is generally required to unfreeze such variables and explore other unseen regions of the configuration space. Here, we introduce a quantum-inspired family of nonlocal Nonequilibrium Monte Carlo (NMC) algorithms by developing an adaptive gradient-free strategy that can efficiently learn key instance-wise geometrical features of the cost function. That information is employed on-the-fly to construct spatially inhomogeneous thermal fluctuations for collectively unfreezing variables at various length scales, circumventing costly exploration versus exploitation trade-offs. We apply our algorithm to two of the most challenging combinatorial optimization problems: random k-satisfiability (k-SAT) near the computational phase transitions and Quadratic Assignment Problems (QAP). We observe significant speedup and robustness over both specialized deterministic solvers and generic stochastic solvers. In particular, for 90% of random 4-SAT instances we find solutions that are inaccessible for the best specialized deterministic algorithm known as Survey Propagation (SP) with an order of magnitude improvement in the quality of solutions for the hardest 10% instances. We also demonstrate two orders of magnitude improvement in time-to-solution over the state-of-the-art generic stochastic solver known as Adaptive Parallel Tempering (APT). △ Less

Submitted 26 November, 2021; originally announced November 2021.

Comments: 28 pages, 18 figures

Classical analog of qubit logic based on a magnon Bose-Einstein condensate

Authors: Morteza Mohseni, Vitaliy I. Vasyuchka, Victor S. L'vov, Alexander A. Serga, Burkard Hillebrands

Abstract: We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate formed at opposite wavevectors in a room-temperature yttrium-iron-garnet ferrimagnetic film. The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit. Solving the Gross-… ▽ More We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate formed at opposite wavevectors in a room-temperature yttrium-iron-garnet ferrimagnetic film. The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit. Solving the Gross-Pitaevskii equation and employing micromagnetic numerical simulations, we first show how to initialize the system in one of the basis states: the application of wavevector-selective parallel parametric pumping allows us to form only a single condensate in one of the two lowest energy states of the magnon gas. Next, by translating the concept of Rabi-oscillations into the wavevector domain, we demonstrate how to manipulate the magnon-BEC system along the polar axis in the Bloch sphere representation. We also discuss the manipulation regarding the azimuthal angle. △ Less

Submitted 7 January, 2022; v1 submitted 12 November, 2021; originally announced November 2021.

Comments: 3 figures

Journal ref: Communications Physics 5, 196 (2022)

Sampling diverse near-optimal solutions via algorithmic quantum annealing

Authors: Masoud Mohseni, Marek M. Rams, Sergei V. Isakov, Daniel Eppens, Susanne Pielawa, Johan Strumpfer, Sergio Boixo, Hartmut Neven

Abstract: Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open problems is the lack of ergodicity, or mode collapse, for typical stochastic solvers based on Monte Carlo techniques leading to poor generalization or lack of ro… ▽ More Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open problems is the lack of ergodicity, or mode collapse, for typical stochastic solvers based on Monte Carlo techniques leading to poor generalization or lack of robustness to uncertainties. Currently, there is no universal metric to quantify such performance deficiencies across various solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems. Among others, it allows benchmarking solver performance by a required time-to-diversity (TTD), a generalization of often used time-to-solution (TTS). We illustrate this metric by comparing the sampling power of various quantum annealing strategies. In particular, we show that the inhomogeneous quantum annealing schedules can redistribute and suppress the emergence of topological defects by controlling space-time separated critical fronts, leading to an advantage over standard quantum annealing schedules with respect to both TTS and TTD for finding rare solutions. Using path-integral Monte Carlo simulations for up to 1600 qubits, we demonstrate that nonequilibrium driving of quantum fluctuations, guided by efficient approximate tensor network contractions, can significantly reduce the fraction of hard instances for random frustrated 2D spin-glasses with local fields. Specifically, we observe that by creating a class of algorithmic quantum phase transitions, the diversity of solutions can be enhanced by up to 40% with the fraction of hard-to-sample instances reducing by more than 25%. △ Less

Submitted 11 January, 2024; v1 submitted 20 October, 2021; originally announced October 2021.

Comments: 13 pages, 6 figures, close to published version

Journal ref: Phys. Rev. E 108, 065303 (2023)

Diversity metric for evaluation of quantum annealing

Authors: Alex Zucca, Hossein Sadeghi, Masoud Mohseni, Mohammad H. Amin

Abstract: Solving discrete NP-hard problems is an important part of scientific discoveries and operations research as well as many commercial applications. A commonly used metric to compare meta-heuristic solvers is the time required to obtain an optimal solution, known as time to solution. However, for some applications it is desirable to have a set of high-quality and diverse solutions, instead of a singl… ▽ More Solving discrete NP-hard problems is an important part of scientific discoveries and operations research as well as many commercial applications. A commonly used metric to compare meta-heuristic solvers is the time required to obtain an optimal solution, known as time to solution. However, for some applications it is desirable to have a set of high-quality and diverse solutions, instead of a single optimal one. For these applications, time to solution may not be informative of the performance of a solver, and another metric would be necessary. In particular, it is not known how well quantum solvers sample the configuration space in comparison to their classical counterparts. Here, we apply a recently introduced collective distance measure in solution space to quantify diversity by Mohseni et. al. and, based on that, we employ time-to-diversity as a metric for evaluation of meta-heuristics solvers. We use this measure to compare the performance of the D-Wave quantum annealing processor with a few classical heuristic solvers on a set of synthetic problems and show that D-Wave quantum annealing processor is indeed a competitive heuristic, and on many instances outperforms state-of-the-art classical solvers, while it remains on par on other instances. This suggests that a portfolio solver that combines quantum and classical solutions may win over all solvers. △ Less

Submitted 22 October, 2021; v1 submitted 19 October, 2021; originally announced October 2021.

Comments: 14 pages, 9 figures

Observation of Time-Crystalline Eigenstate Order on a Quantum Processor

Authors: Xiao Mi, Matteo Ippoliti, Chris Quintana, Ami Greene, Zijun Chen, Jonathan Gross, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Alexander Bilmes, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Dripto Debroy , et al. (80 additional authors not shown)

Abstract: Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dyn… ▽ More Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors. △ Less

Submitted 11 August, 2021; v1 submitted 28 July, 2021; originally announced July 2021.

Journal ref: Nature 601, 531 (2022)

Entangling Quantum Generative Adversarial Networks

Authors: Murphy Yuezhen Niu, Alexander Zlokapa, Michael Broughton, Sergio Boixo, Masoud Mohseni, Vadim Smelyanskyi, Hartmut Neven

Abstract: Generative adversarial networks (GANs) are one of the most widely adopted semisupervised and unsupervised machine learning methods for high-definition image, video, and audio generation. In this work, we propose a new type of architecture for quantum generative adversarial networks (entangling quantum GAN, EQ-GAN) that overcomes some limitations of previously proposed quantum GANs. Leveraging the… ▽ More Generative adversarial networks (GANs) are one of the most widely adopted semisupervised and unsupervised machine learning methods for high-definition image, video, and audio generation. In this work, we propose a new type of architecture for quantum generative adversarial networks (entangling quantum GAN, EQ-GAN) that overcomes some limitations of previously proposed quantum GANs. Leveraging the entangling power of quantum circuits, EQ-GAN guarantees the convergence to a Nash equilibrium under minimax optimization of the discriminator and generator circuits by performing entangling operations between both the generator output and true quantum data. We show that EQ-GAN has additional robustness against coherent errors and demonstrate the effectiveness of EQ-GAN experimentally in a Google Sycamore superconducting quantum processor. By adversarially learning efficient representations of quantum states, we prepare an approximate quantum random access memory (QRAM) and demonstrate its use in applications including the training of quantum neural networks. △ Less

Submitted 23 May, 2021; v1 submitted 30 April, 2021; originally announced May 2021.

Realizing topologically ordered states on a quantum processor

Authors: K. J. Satzinger, Y. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, C. Gidney, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, R. Barends, J. Basso, A. Bengtsson, A. Bilmes, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett , et al. (73 additional authors not shown)

Abstract: The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an effi… ▽ More The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction. △ Less

Submitted 2 April, 2021; originally announced April 2021.

Comments: 6 pages 4 figures, plus supplementary materials

Journal ref: Science 374, 1237-1241 (2021)

Exponential suppression of bit or phase flip errors with repetitive error correction

Authors: Zijun Chen, Kevin J. Satzinger, Juan Atalaya, Alexander N. Korotkov, Andrew Dunsworth, Daniel Sank, Chris Quintana, Matt McEwen, Rami Barends, Paul V. Klimov, Sabrina Hong, Cody Jones, Andre Petukhov, Dvir Kafri, Sean Demura, Brian Burkett, Craig Gidney, Austin G. Fowler, Harald Putterman, Igor Aleiner, Frank Arute, Kunal Arya, Ryan Babbush, Joseph C. Bardin, Andreas Bengtsson , et al. (66 additional authors not shown)

Abstract: Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so t… ▽ More Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing. △ Less

Submitted 11 February, 2021; originally announced February 2021.

Journal ref: Nature volume 595, pages 383-387 (2021)

Machine learning of high dimensional data on a noisy quantum processor

Authors: Evan Peters, João Caldeira, Alan Ho, Stefan Leichenauer, Masoud Mohseni, Hartmut Neven, Panagiotis Spentzouris, Doug Strain, Gabriel N. Perdue

Abstract: We present a quantum kernel method for high-dimensional data analysis using Google's universal quantum processor, Sycamore. This method is successfully applied to the cosmological benchmark of supernova classification using real spectral features with no dimensionality reduction and without vanishing kernel elements. Instead of using a synthetic dataset of low dimension or pre-processing the data… ▽ More We present a quantum kernel method for high-dimensional data analysis using Google's universal quantum processor, Sycamore. This method is successfully applied to the cosmological benchmark of supernova classification using real spectral features with no dimensionality reduction and without vanishing kernel elements. Instead of using a synthetic dataset of low dimension or pre-processing the data with a classical machine learning algorithm to reduce the data dimension, this experiment demonstrates that machine learning with real, high dimensional data is possible using a quantum processor; but it requires careful attention to shot statistics and mean kernel element size when constructing a circuit ansatz. Our experiment utilizes 17 qubits to classify 67 dimensional data - significantly higher dimensionality than the largest prior quantum kernel experiments - resulting in classification accuracy that is competitive with noiseless simulation and comparable classical techniques. △ Less

Submitted 23 January, 2021; originally announced January 2021.

Comments: 20 pages, 12 figures

Report number: FERMILAB-PUB-20-624-QIS

Information Scrambling in Computationally Complex Quantum Circuits

Authors: Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandra, Jeffrey Marshall, Charles Neill, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Alexandre Bourassa, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura , et al. (68 additional authors not shown)

Abstract: Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum… ▽ More Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish the two mechanisms associated with quantum scrambling, operator spreading and operator entanglement, and experimentally observe their respective signatures. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors. △ Less

Submitted 21 January, 2021; originally announced January 2021.

Journal ref: Science 374, 1479 (2021)

Accurately computing electronic properties of a quantum ring

Authors: C. Neill, T. McCourt, X. Mi, Z. Jiang, M. Y. Niu, W. Mruczkiewicz, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, R. Barends, A. Bengtsson, A. Bourassa, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, J. Campero, Z. Chen, B. Chiaro, R. Collins, W. Courtney , et al. (67 additional authors not shown)

Abstract: A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to probe fundamental electronic propert… ▽ More A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to probe fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band-structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 rad, whereas typical energy scales are of order 1 rad. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e-4 rad. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensed-matter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits. △ Less

Submitted 1 June, 2021; v1 submitted 1 December, 2020; originally announced December 2020.

Power of data in quantum machine learning

Authors: Hsin-Yuan Huang, Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, Jarrod R. McClean

Abstract: The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. U… ▽ More The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits. △ Less

Submitted 10 February, 2021; v1 submitted 3 November, 2020; originally announced November 2020.

Journal ref: Nature Communications, Vol.12, No. 2631 (2021)

Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Authors: Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Yu-An Chen, Ben Chiaro, Roberto Collins, Stephen J. Cotton, William Courtney, Sean Demura, Alan Derk, Andrew Dunsworth, Daniel Eppens, Thomas Eckl , et al. (74 additional authors not shown)

Abstract: Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate… ▽ More Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices. △ Less

Submitted 15 October, 2020; originally announced October 2020.

Comments: 20 pages, 15 figures

Low depth mechanisms for quantum optimization

Authors: Jarrod R. McClean, Matthew P. Harrigan, Masoud Mohseni, Nicholas C. Rubin, Zhang Jiang, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, Hartmut Neven

Abstract: One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these algorithms based on connections to simple dynamics of quantum systems, quantum walks, and classical continuous relaxations. We focus on developing a language and tools… ▽ More One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these algorithms based on connections to simple dynamics of quantum systems, quantum walks, and classical continuous relaxations. We focus on developing a language and tools connected with kinetic energy on a graph for understanding the physical mechanisms of success and failure to guide algorithmic improvement. This physical language, in combination with uniqueness results related to unitarity, allow us to identify some potential pitfalls from kinetic energy fundamentally opposing the goal of optimization. This is connected to effects from wavefunction confinement, phase randomization, and shadow defects lurking in the objective far away from the ideal solution. As an example, we explore the surprising deficiency of many quantum methods in solving uncoupled spin problems and how this is both predictive of performance on some more complex systems while immediately suggesting simple resolutions. Further examination of canonical problems like the Hamming ramp or bush of implications show that entanglement can be strictly detrimental to performance results from the underlying mechanism of solution in approaches like QAOA. Kinetic energy and graph Laplacian perspectives provide new insights to common initialization and optimal solutions in QAOA as well as new methods for more effective layerwise training. Connections to classical methods of continuous extensions, homotopy methods, and iterated rounding suggest new directions for research in quantum optimization. Throughout, we unveil many pitfalls and mechanisms in quantum optimization using a physical perspective, which aim to spur the development of novel quantum optimization algorithms and refinements. △ Less

Submitted 19 August, 2020; originally announced August 2020.

Journal ref: PRX Quantum 2, 030312 (2021)

Layerwise learning for quantum neural networks

Authors: Andrea Skolik, Jarrod R. McClean, Masoud Mohseni, Patrick van der Smagt, Martin Leib

Abstract: With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum… ▽ More With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training. △ Less

Submitted 26 June, 2020; originally announced June 2020.

Comments: 11 pages, 7 figures

Journal ref: Quantum Machine Intelligence Vol. 3, No. 5 (2021)

Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor

Authors: Matthew P. Harrigan, Kevin J. Sung, Matthew Neeley, Kevin J. Satzinger, Frank Arute, Kunal Arya, Juan Atalaya, Joseph C. Bardin, Rami Barends, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Sean Demura, Andrew Dunsworth, Daniel Eppens, Austin Fowler, Brooks Foxen , et al. (61 additional authors not shown)

Abstract: We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the (planar) connectivity graph of our hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model and MaxCut, both… ▽ More We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the (planar) connectivity graph of our hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model and MaxCut, both high dimensional graph problems for which the QAOA requires significant compilation. Experimental scans of the QAOA energy landscape show good agreement with theory across even the largest instances studied (23 qubits) and we are able to perform variational optimization successfully. For problems defined on our hardware graph we obtain an approximation ratio that is independent of problem size and observe, for the first time, that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size but still provides an advantage over random guessing for circuits involving several thousand gates. This behavior highlights the challenge of using near-term quantum computers to optimize problems on graphs differing from hardware connectivity. As these graphs are more representative of real world instances, our results advocate for more emphasis on such problems in the developing tradition of using the QAOA as a holistic, device-level benchmark of quantum processors. △ Less

Submitted 30 January, 2021; v1 submitted 8 April, 2020; originally announced April 2020.

Comments: 19 pages, 15 figures

Journal ref: Nature Physics 17, 332-336 (2021)

Hartree-Fock on a superconducting qubit quantum computer

Authors: Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura, Andrew Dunsworth, Daniel Eppens, Edward Farhi, Austin Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina , et al. (57 additional authors not shown)

Abstract: As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of ${\rm H}_6$, ${\rm H}_8$,… ▽ More As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of ${\rm H}_6$, ${\rm H}_8$, ${\rm H}_{10}$ and ${\rm H}_{12}$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realize the Givens rotation approach to non-interacting fermion evolution, which we variationally optimize to prepare the Hartree-Fock wavefunction. This ubiquitous algorithmic primitive corresponds to a rotation of the orbital basis and is required by many proposals for correlated simulations of molecules and Hubbard models. Because non-interacting fermion evolutions are classically tractable to simulate, yet still generate highly entangled states over the computational basis, we use these experiments to benchmark the performance of our hardware while establishing a foundation for scaling up more complex correlated quantum simulations of chemistry. △ Less

Submitted 18 September, 2020; v1 submitted 8 April, 2020; originally announced April 2020.

Comments: updated link to experiment code, new version containing expanded data sets and corrected figure label

Journal ref: Science 369 (6507), 1084-1089, 2020

TensorFlow Quantum: A Software Framework for Quantum Machine Learning

Authors: Michael Broughton, Guillaume Verdon, Trevor McCourt, Antonio J. Martinez, Jae Hyeon Yoo, Sergei V. Isakov, Philip Massey, Ramin Halavati, Murphy Yuezhen Niu, Alexander Zlokapa, Evan Peters, Owen Lockwood, Andrea Skolik, Sofiene Jerbi, Vedran Dunjko, Martin Leib, Michael Streif, David Von Dollen, Hongxiang Chen, Shuxiang Cao, Roeland Wiersema, Hsin-Yuan Huang, Jarrod R. McClean, Ryan Babbush, Sergio Boixo , et al. (4 additional authors not shown)

Abstract: We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software archi… ▽ More We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage. △ Less

Submitted 26 August, 2021; v1 submitted 5 March, 2020; originally announced March 2020.

Comments: 56 pages, 34 figures, many updates throughout the manuscript, several new sections are added

Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms

Authors: B. Foxen, C. Neill, A. Dunsworth, P. Roushan, B. Chiaro, A. Megrant, J. Kelly, Zijun Chen, K. Satzinger, R. Barends, F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, S. Boixo, D. Buell, B. Burkett, Yu Chen, R. Collins, E. Farhi, A. Fowler, C. Gidney, M. Giustina, R. Graff , et al. (32 additional authors not shown)

Abstract: Quantum algorithms offer a dramatic speedup for computational problems in machine learning, material science, and chemistry. However, any near-term realizations of these algorithms will need to be heavily optimized to fit within the finite resources offered by existing noisy quantum hardware. Here, taking advantage of the strong adjustable coupling of gmon qubits, we demonstrate a continuous two-q… ▽ More Quantum algorithms offer a dramatic speedup for computational problems in machine learning, material science, and chemistry. However, any near-term realizations of these algorithms will need to be heavily optimized to fit within the finite resources offered by existing noisy quantum hardware. Here, taking advantage of the strong adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a 3x reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an iSWAP-like gate to attain an arbitrary swap angle, $θ$, and a CPHASE gate that generates an arbitrary conditional phase, $φ$. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic Simulation, or fSim, gate set. We benchmark the fidelity of the iSWAP-like and CPHASE gate families as well as 525 other fSim gates spread evenly across the entire fSim($θ$, $φ$) parameter space achieving purity-limited average two-qubit Pauli error of $3.8 \times 10^{-3}$ per fSim gate. △ Less

Submitted 3 February, 2020; v1 submitted 22 January, 2020; originally announced January 2020.

Comments: 20 pages, 17 figures

Journal ref: Phys. Rev. Lett. 125, 120504 (2020)

A Probability Density Theory for Spin-Glass Systems

Authors: Gavin S. Hartnett, Masoud Mohseni

Abstract: Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of spin-glass systems. In general, evaluating the relevant physical and computational properties of such models is difficult due to critical slowing down near a phase tra… ▽ More Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of spin-glass systems. In general, evaluating the relevant physical and computational properties of such models is difficult due to critical slowing down near a phase transition. Ideally, one could use recent advances in deep learning for characterizing the low-energy properties of these complex systems. Unfortunately, many of the most promising machine learning approaches are only valid for distributions over continuous variables and thus cannot be directly applied to discrete spin-glass models. To this end, we develop a continuous probability density theory for spin-glass systems with arbitrary dimensions, interactions, and local fields. We show how our formulation geometrically encodes key physical and computational properties of the spin-glass in an instance-wise fashion without the need for quenched disorder averaging. We show that our approach is beyond the mean-field theory and identify a transition from a convex to non-convex energy landscape as the temperature is lowered past a critical temperature. We apply our formalism to a number of spin-glass models including the Sherrington-Kirkpatrick (SK) model, spins on random Erdős-Rényi graphs, and random restricted Boltzmann machines. △ Less

Submitted 10 January, 2020; v1 submitted 3 January, 2020; originally announced January 2020.

Comments: 20 pages, 5 figures

Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows

Authors: Gavin S. Hartnett, Masoud Mohseni

Abstract: Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning. Computing the underlying structure and dynamics of such complex systems is extremely difficult due to the combinatorial explosion of their state space. Here, we… ▽ More Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning. Computing the underlying structure and dynamics of such complex systems is extremely difficult due to the combinatorial explosion of their state space. Here, we develop deep generative continuous spin-glass distributions with normalizing flows to model correlations in generic discrete problems. We use a self-supervised learning paradigm by automatically generating the data from the spin-glass itself. We demonstrate that key physical and computational properties of the spin-glass phase can be successfully learned, including multi-modal steady-state distributions and topological structures among metastable states. Remarkably, we observe that the learning itself corresponds to a spin-glass phase transition within the layers of the trained normalizing flows. The inverse normalizing flows learns to perform reversible multi-scale coarse-graining operations which are very different from the typical irreversible renormalization group techniques. △ Less

Submitted 10 January, 2020; v1 submitted 2 January, 2020; originally announced January 2020.

Comments: 16 pages, 7 figures

Scaling advantage in quantum simulation of geometrically frustrated magnets

Authors: Andrew D. King, Jack Raymond, Trevor Lanting, Sergei V. Isakov, Masoud Mohseni, Gabriel Poulin-Lamarre, Sara Ejtemaee, William Bernoudy, Isil Ozfidan, Anatoly Yu. Smirnov, Mauricio Reis, Fabio Altomare, Michael Babcock, Catia Baron, Andrew J. Berkley, Kelly Boothby, Paul I. Bunyk, Holly Christiani, Colin Enderud, Bram Evert, Richard Harris, Emile Hoskinson, Shuiyuan Huang, Kais Jooya, Ali Khodabandelou , et al. (29 additional authors not shown)

Abstract: The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observa… ▽ More The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of relaxation in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) relaxation timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation over the classical approach of path-integral Monte Carlo (PIMC) fixed-Hamiltonian relaxation with multiqubit cluster updates. The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over a CPU. This is an important piece of experimental evidence that in general, PIMC does not mimic QA dynamics for stoquastic Hamiltonians. The observed scaling advantage, for simulation of frustrated magnetism in quantum condensed matter, demonstrates that near-term quantum devices can be used to accelerate computational tasks of practical relevance. △ Less

Submitted 8 November, 2019; originally announced November 2019.

Comments: 7 pages, 4 figures, 22 pages of supplemental material with 18 figures

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

Authors: Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G. S. L. Brandao, David A. Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger , et al. (52 additional authors not shown)

Abstract: This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at https://www.nature.com/articles/s41586-019-1666-5. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Er… ▽ More This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at https://www.nature.com/articles/s41586-019-1666-5. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections. △ Less

Submitted 28 December, 2019; v1 submitted 23 October, 2019; originally announced October 2019.

Comments: 67 pages, 51 figures

Journal ref: Nature, Vol 574, 505 (2019)

Direct measurement of non-local interactions in the many-body localized phase

Authors: B. Chiaro, C. Neill, A. Bohrdt, M. Filippone, F. Arute, K. Arya, R. Babbush, D. Bacon, J. Bardin, R. Barends, S. Boixo, D. Buell, B. Burkett, Y. Chen, Z. Chen, R. Collins, A. Dunsworth, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, M. Harrigan, T. Huang, S. Isakov , et al. (36 additional authors not shown)

Abstract: The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these p… ▽ More The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two qubit density matrices allowed us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here measure affirmative correlations and allow us to exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter. △ Less

Submitted 8 July, 2020; v1 submitted 14 October, 2019; originally announced October 2019.

Comments: 5+28 pages, 5+22 figures, updated version

Learning to learn with quantum neural networks via classical neural networks

Authors: Guillaume Verdon, Michael Broughton, Jarrod R. McClean, Kevin J. Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, Masoud Mohseni

Abstract: Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization heuristics that ensure rapid and consistent convergence to local minima of the parameterized quantum circuit landscape. In this work, we train classical neural… ▽ More Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization heuristics that ensure rapid and consistent convergence to local minima of the parameterized quantum circuit landscape. In this work, we train classical neural networks to assist in the quantum learning process, also know as meta-learning, to rapidly find approximate optima in the parameter landscape for several classes of quantum variational algorithms. Specifically, we train classical recurrent neural networks to find approximately optimal parameters within a small number of queries of the cost function for the Quantum Approximate Optimization Algorithm (QAOA) for MaxCut, QAOA for Sherrington-Kirkpatrick Ising model, and for a Variational Quantum Eigensolver for the Hubbard model. By initializing other optimizers at parameter values suggested by the classical neural network, we demonstrate a significant improvement in the total number of optimization iterations required to reach a given accuracy. We further demonstrate that the optimization strategies learned by the neural network generalize well across a range of problem instance sizes. This opens up the possibility of training on small, classically simulatable problem instances, in order to initialize larger, classically intractably simulatable problem instances on quantum devices, thereby significantly reducing the number of required quantum-classical optimization iterations. △ Less

Submitted 11 July, 2019; originally announced July 2019.

Comments: 12 pages, 4 figures

Quantum-Assisted Genetic Algorithm

Authors: James King, Masoud Mohseni, William Bernoudy, Alexandre Fréchette, Hossein Sadeghi, Sergei V. Isakov, Hartmut Neven, Mohammad H. Amin

Abstract: Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Revers… ▽ More Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Reverse annealing enables the development of genetic algorithms that use quantum fluctuation for mutations and classical mechanisms for the crossovers -- we refer to these as Quantum-Assisted Genetic Algorithms (QAGAs). We describe a QAGA and present experimental results using a D-Wave 2000Q quantum annealing processor. On a set of spin-glass inputs, standard (forward) quantum annealing finds good solutions very quickly but struggles to find global optima. In contrast, our QAGA proves effective at finding global optima for these inputs. This successful interplay of non-local classical and quantum fluctuations could provide a promising step toward practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices for heuristic discrete optimization. △ Less

Submitted 24 June, 2019; originally announced July 2019.

Comments: 13 pages, 5 figures, presented at AQC 2019

Variational Quantum Unsampling on a Quantum Photonic Processor

Authors: Jacques Carolan, Masoud Mohseni, Jonathan P. Olson, Mihika Prabhu, Changchen Chen, Darius Bunandar, Nicholas C. Harris, Franco N. C. Wong, Michael Hochberg, Seth Lloyd, Dirk Englund

Abstract: Quantum algorithms for Noisy Intermediate-Scale Quantum (NISQ) machines have recently emerged as new promising routes towards demonstrating near-term quantum advantage (or supremacy) over classical systems. In these systems samples are typically drawn from probability distributions which --- under plausible complexity-theoretic conjectures --- cannot be efficiently generated classically. Rather th… ▽ More Quantum algorithms for Noisy Intermediate-Scale Quantum (NISQ) machines have recently emerged as new promising routes towards demonstrating near-term quantum advantage (or supremacy) over classical systems. In these systems samples are typically drawn from probability distributions which --- under plausible complexity-theoretic conjectures --- cannot be efficiently generated classically. Rather than first define a physical system and then determine computational features of the output state, we ask the converse question: given direct access to the quantum state, what features of the generating system can we efficiently learn? In this work we introduce the Variational Quantum Unsampling (VQU) protocol, a nonlinear quantum neural network approach for verification and inference of near-term quantum circuits outputs. In our approach one can variationally train a quantum operation to unravel the action of an unknown unitary on a known input state; essentially learning the inverse of the black-box quantum dynamics. While the principle of our approach is platform independent, its implementation will depend on the unique architecture of a specific quantum processor. Here, we experimentally demonstrate the VQU protocol on a quantum photonic processor. Alongside quantum verification, our protocol has broad applications; including optimal quantum measurement and tomography, quantum sensing and imaging, and ansatz validation. △ Less

Submitted 13 May, 2019; v1 submitted 23 April, 2019; originally announced April 2019.

Comments: Comments welcome. Updates references and acknowledgements

Approximate optimization, sampling and spin-glass droplets discovery with tensor networks

Authors: Marek M. Rams, Masoud Mohseni, Daniel Eppens, Konrad Jałowiecki, Bartłomiej Gardas

Abstract: We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible configurations. Using approximate tensor-network contractions, we are able to efficiently map the low-energy spectrum of some quasi-two-dimensional Hamiltonians. We exploi… ▽ More We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible configurations. Using approximate tensor-network contractions, we are able to efficiently map the low-energy spectrum of some quasi-two-dimensional Hamiltonians. We exploit the local nature of the problems to compute spin-glass droplets geometries, which provides a new form of compression of the low-energy spectrum. It naturally extends to sampling, which otherwise, for exact contraction, is $\#$P-complete. In particular, for one of the hardest known problem-classes devised on chimera graphs known as deceptive cluster loops and for up to $2048$ spins, we find on the order of $10^{10}$ degenerate ground states in a single run of our algorithm, computing better solutions than have been reported on some hard instances. Our gradient-free approach could provide new insight into the structure of disordered spin-glass complexes, with ramifications both for machine learning and noisy intermediate-scale quantum devices. △ Less

Submitted 6 September, 2021; v1 submitted 15 November, 2018; originally announced November 2018.

Comments: Final version; 7+6 pages, 4+6 figures; added benchmarks on time-to-solution and fair sampling/counting versus PT and QA. Code and problem instances can be found at https://github.com/marekrams/tnac4o

Journal ref: Phys. Rev. E 104, 025308 (2021)

Efficient population transfer via non-ergodic extended states in quantum spin glass

Authors: Kostyantyn Kechedzhi, Vadim Smelyanskiy, Jarrod R. McClean, Vasil S. Denchev, Masoud Mohseni, Sergei Isakov, Sergio Boixo, Boris Altshuler, Hartmut Neven

Abstract: We analyze a new computational role of coherent multi-qubit quantum tunneling that gives rise to bands of non-ergodic extended (NEE) quantum states each formed by a superposition of a large number of computational states (deep local minima of the energy landscape) with similar energies. NEE provide a mechanism for population transfer (PT) between computational states and therefore can serve as a n… ▽ More We analyze a new computational role of coherent multi-qubit quantum tunneling that gives rise to bands of non-ergodic extended (NEE) quantum states each formed by a superposition of a large number of computational states (deep local minima of the energy landscape) with similar energies. NEE provide a mechanism for population transfer (PT) between computational states and therefore can serve as a new quantum subroutine for quantum search, quantum parallel tempering and reverse annealing optimization algorithms. We study PT in a quantum n-spin system subject to a transverse field where the energy function $E(z)$ encodes a classical optimization problem over the set of spin configurations $z$. Given an initial spin configuration with low energy, PT protocol searches for other bitstrings at energies within a narrow window around the initial one. We provide an analytical solution for PT in a simple yet nontrivial model: $M$ randomly chosen marked bit-strings are assigned energies $E(z)$ within a narrow strip $[-n -W/2, n + W/2]$, while the rest of the states are assigned energy 0. We find that the scaling of a typical PT runtime with n and L is the same as that in the multi-target Grover's quantum search algorithm, except for a factor that is equal to $\exp(n /(2B^2))$ for finite transverse field $B\gg1$. Unlike the Hamiltonians used in analog quantum unstructured search algorithms known so far, the model we consider is non-integrable and population transfer is not exponentially sensitive in n to the weight of the driver Hamiltonian. We study numerically the PT subroutine as a part of quantum parallel tempering algorithm for a number of examples of binary optimization problems on fully connected graphs. △ Less

Submitted 12 July, 2018; originally announced July 2018.

Comments: 16 pages, 7 figures; proceedings of TQC 2018

Universal discriminative quantum neural networks

Authors: Hongxiang Chen, Leonard Wossnig, Simone Severini, Hartmut Neven, Masoud Mohseni

Abstract: Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optim… ▽ More Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown non-unitary quantum circuit. This circuit learns to simulates the unknown structure of a generalized quantum measurement, or Positive-Operator-Value-Measure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we use universal circuit topologies, with a theoretically motivated circuit design, which guarantees that our circuits can in principle learn to perform arbitrary input-output mappings. Our numerical simulations show that shallow quantum circuits could be trained to discriminate among various pure and mixed quantum states exhibiting a trade-off between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We train the circuit on different classes of quantum data and evaluate the generalization error on unseen mixed quantum states. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue. △ Less

Submitted 22 May, 2018; originally announced May 2018.

Comments: 19 pages, 10 figures

Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians

Authors: Masoud Mohseni, Johan Strumpfer, Marek M. Rams

Abstract: We introduce a phenomenological theory for many-body control of critical phenomena by engineering causally-induced gaps for quantum Hamiltonian systems. The core mechanisms are controlling information flow within and/or between clusters that are created near a quantum critical point. To this end, we construct inhomogeneous quantum phase transitions via designing spatio-temporal quantum fluctuation… ▽ More We introduce a phenomenological theory for many-body control of critical phenomena by engineering causally-induced gaps for quantum Hamiltonian systems. The core mechanisms are controlling information flow within and/or between clusters that are created near a quantum critical point. To this end, we construct inhomogeneous quantum phase transitions via designing spatio-temporal quantum fluctuations. We show how non-equilibrium evolution of disordered quantum systems can create new effective correlation length scales and effective dynamical critical exponents. In particular, we construct a class of causally-induced non-adiabatic quantum annealing transitions for strongly disordered quantum Ising chains leading to exponential suppression of topological defects beyond standard Kibble-Zurek predictions. Using exact numerical techniques for 1D quantum Hamiltonian systems, we demonstrate that our approach exponentially outperform adiabatic quantum computing. Using Strong-Disorder Renormalization Group (SDRG), we demonstrate the universality of inhomogeneous quantum critical dynamics and exhibit the causal zones reconstructions during SDRG flow. We derive a scaling relation for minimal causal gaps showing they narrow more slowly than any polynomial with increasing size of system, in contrast to stretched exponential scaling in standard adiabatic evolution. Furthermore, we demonstrate similar scaling behaviour for random cluster-Ising Hamiltonians with higher order interactions. △ Less

Submitted 19 October, 2018; v1 submitted 29 April, 2018; originally announced April 2018.

Comments: 16 pages, 9 figures, minor corrections, close to the published version

Journal ref: New J. Phys. 20, 105002 (2018)

Environment-assisted analog quantum search

Authors: Leonardo Novo, Shantanav Chakraborty, Masoud Mohseni, Yasser Omar

Abstract: Two main obstacles for observing quantum advantage in noisy intermediate-scale quantum computers (NISQ) are the finite precision effects due to control errors, or disorders, and decoherence effects due to thermal fluctuations. It has been shown that dissipative quantum computation is possible in presence of an idealized fully-engineered bath. However, it is not clear, in general, what performance… ▽ More Two main obstacles for observing quantum advantage in noisy intermediate-scale quantum computers (NISQ) are the finite precision effects due to control errors, or disorders, and decoherence effects due to thermal fluctuations. It has been shown that dissipative quantum computation is possible in presence of an idealized fully-engineered bath. However, it is not clear, in general, what performance can be achieved by NISQ when internal bath degrees of freedom are not controllable. In this work, we consider the task of quantum search of a marked node on a complete graph of $n$ nodes in the presence of both static disorder and non-zero coupling to an environment. We show that, given fixed and finite levels of disorder and thermal fluctuations, there is an optimal range of bath temperatures that can significantly improve the success probability of the algorithm. Remarkably for a fixed disorder strength $σ$, the system relaxation time decreases for higher temperatures within a robust range of parameters. In particular, we demonstrate that for strong disorder, the presence of a thermal bath increases the success probability from $1/(n σ^2)$ to at least $1/2$. While the asymptotic running time is approximately maintained, the need to repeat the algorithm many times and issues associated with unitary over-rotations can be avoided as the system relaxes to an absorbing steady state. Furthermore, we discuss for what regimes of disorder and bath parameters quantum speedup is possible and mention conditions for which similar phenomena can be observed in more general families of graphs. Our work highlights that in the presence of static disorder, even non-engineered environmental interactions can be beneficial for a quantum algorithm. △ Less

Submitted 13 August, 2018; v1 submitted 5 October, 2017; originally announced October 2017.

Journal ref: Phys. Rev. A 98, 022316 (2018)

Quantum control of topological defects in magnetic systems

Authors: So Takei, Masoud Mohseni

Abstract: Energy-efficient classical information processing and storage based on topological defects in magnetic systems have been studied over past decade. In this work, we introduce a class of macroscopic quantum devices in which a quantum state is stored in a topological defect of a magnetic insulator. We propose non-invasive methods to coherently control and readout the quantum state using ac magnetic f… ▽ More Energy-efficient classical information processing and storage based on topological defects in magnetic systems have been studied over past decade. In this work, we introduce a class of macroscopic quantum devices in which a quantum state is stored in a topological defect of a magnetic insulator. We propose non-invasive methods to coherently control and readout the quantum state using ac magnetic fields and magnetic force microscopy, respectively. This macroscopic quantum spintronic device realizes the magnetic analog of the three-level rf-SQUID qubit and is built fully out of electrical insulators with no mobile electrons, thus eliminating decoherence due to the coupling of the quantum variable to an electronic continuum and energy dissipation due to Joule heating. For a domain wall sizes of $10-100$~nm and reasonable material parameters, we estimate qubit operating temperatures in the range of $0.1-1$~K, a decoherence time of about $0.01-1$~$μ$s, and the number of Rabi flops within the coherence time scale in the range of $10^{2}-10^{4}$. △ Less

Submitted 5 February, 2018; v1 submitted 5 June, 2017; originally announced June 2017.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. B 97, 064401 (2018)

Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains

Authors: Marek M. Rams, Masoud Mohseni, Adolfo del Campo

Abstract: We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The… ▽ More We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude. △ Less

Submitted 27 December, 2016; v1 submitted 24 June, 2016; originally announced June 2016.

Comments: 10 pages, 7 figures, published version

Journal ref: New J. Phys. 18, 123034 (2016)