-
High-rate qLDPC processors
Authors:
Aditya Bhardwaj,
Muzhou Ma,
Nadine Meister,
Robbie King,
Dolev Bluvstein,
John Preskill,
Madelyn Cain,
Qian Xu,
Hsin-Yuan Huang
Abstract:
Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate $20\%$ and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constrainin…
▽ More
Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate $20\%$ and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance $18$ and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the $[\![300,60,14]\!]$ mitten code achieves, without extrapolation, a block logical error rate of ${\sim}10^{-11}$ per round at $0.1\%$ physical error rate (PER), while the $[\![ 975,195,\leq 24 ]\!]$ code reaches ${\sim}10^{-8}$ at $0.4\%$ PER. Decoding $15$ billion surgery experiments on the $[\![540,108,18]\!]$ code at $0.1\%$ PER, we observe only two logical failures, demonstrating a qLDPC processor capable of running ${\sim}10^{10}$ logical operations. Our decoder is compatible with sub-millisecond average latency per logical cycle, sufficient for real-time decoding on neutral atom hardware. Discovered by an end-to-end design pipeline built on sQetch, a distance estimator orders of magnitude faster than existing tools, and mapping efficiently onto near-term neutral atom and superconducting hardware, mitten codes open a practical path toward fault-tolerant quantum computation.
△ Less
Submitted 30 July, 2026;
originally announced July 2026.
-
Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits
Authors:
Madelyn Cain,
Qian Xu,
Robbie King,
Lewis R. B. Picard,
Harry Levine,
Manuel Endres,
John Preskill,
Hsin-Yuan Huang,
Dolev Bluvstein
Abstract:
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance and practical relevance to cryptography. However, due to the high overhead of quantum error correction, optimized resource estimates for cryptographically releva…
▽ More
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance and practical relevance to cryptography. However, due to the high overhead of quantum error correction, optimized resource estimates for cryptographically relevant instances of Shor's algorithm require millions of physical qubits. Here, by leveraging advances in high-rate quantum error-correcting codes, efficient logical instruction sets, and circuit design, we show that Shor's algorithm can be executed at cryptographically relevant scales with as few as 10,000 reconfigurable atomic qubits. Increasing the number of physical qubits improves time efficiency by enabling greater parallelism; under plausible assumptions, the runtime for discrete logarithms on the P-256 elliptic curve could be just a few days for a system with 26,000 physical qubits, while the runtime for factoring RSA-2048 integers is one to two orders of magnitude longer. Recent neutral-atom experiments have demonstrated universal fault-tolerant operations below the error-correction threshold, computation on arrays of hundreds of qubits, and trapping arrays with more than 6,000 highly coherent qubits. Although substantial engineering challenges remain, our theoretical analysis indicates that an appropriately designed neutral-atom architecture could support quantum computation at cryptographically relevant scales. More broadly, these results highlight the capability of neutral atoms for fault-tolerant quantum computing with wide-ranging scientific and technological applications.
△ Less
Submitted 30 March, 2026;
originally announced March 2026.
-
Batched high-rate logical operations for quantum LDPC codes
Authors:
Qian Xu,
Hengyun Zhou,
Dolev Bluvstein,
Madelyn Cain,
Marcin Kalinowski,
John Preskill,
Mikhail D. Lukin,
Nishad Maskara
Abstract:
High-rate quantum LDPC (qLDPC) codes reduce memory overhead by densely packing many logical qubits into a single block of physical qubits. Here we extend this concept to high-rate computation by constructing \emph{batched} fault-tolerant operations that apply the same logical gate across many code blocks in parallel. By leveraging shared physical resources to execute many logical operations in par…
▽ More
High-rate quantum LDPC (qLDPC) codes reduce memory overhead by densely packing many logical qubits into a single block of physical qubits. Here we extend this concept to high-rate computation by constructing \emph{batched} fault-tolerant operations that apply the same logical gate across many code blocks in parallel. By leveraging shared physical resources to execute many logical operations in parallel, these operations realize high rates in space-time and significantly reduce computational costs. For \emph{arbitrary} CSS qLDPC codes, we build batched gadgets with \emph{constant space-time overhead} (assuming fast classical computation) for (i) single-shot error correction, state preparation, and code surgeries (ii) code switching, and (iii) addressable Clifford gates. Using these batched gadgets we also construct parallel non-Clifford gates with low space-time cost. We outline principles for designing parallel quantum algorithms optimized for a batched architecture, and show in particular how lattice Hamiltonian dynamical simulations can be compiled efficiently. We also propose a near-term implementation using new self-dual Bivariate-Bicycle codes with high encoding rates ($\sim 1/10$), transversal Clifford gates, and global $T$ gates via parallel magic state cultivation, enabling Hamiltonian simulations with a lower space-time cost than analogous surface-code protocols and low-rate qLDPC protocols. These results open new paths toward scalable quantum computation via co-design of parallel quantum algorithms and high-rate fault-tolerant protocols.
△ Less
Submitted 7 October, 2025;
originally announced October 2025.
-
Architectural mechanisms of a universal fault-tolerant quantum computer
Authors:
Dolev Bluvstein,
Alexandra A. Geim,
Sophie H. Li,
Simon J. Evered,
J. Pablo Bonilla Ataides,
Gefen Baranes,
Andi Gu,
Tom Manovitz,
Muqing Xu,
Marcin Kalinowski,
Shayan Majidy,
Christian Kokail,
Nishad Maskara,
Elias C. Trapp,
Luke M. Stewart,
Simon Hollerith,
Hengyun Zhou,
Michael J. Gullans,
Susanne F. Yelin,
Markus Greiner,
Vladan Vuletic,
Madelyn Cain,
Mikhail D. Lukin
Abstract:
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of…
▽ More
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement all key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors, demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding. We then investigate logical entanglement using transversal gates and lattice surgery, and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes, enabling arbitrary-angle synthesis with logarithmic overhead. Finally, we develop mid-circuit qubit re-use, increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic and entropy removal, judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.
△ Less
Submitted 25 June, 2025;
originally announced June 2025.
-
Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays
Authors:
Hengyun Zhou,
Casey Duckering,
Chen Zhao,
Dolev Bluvstein,
Madelyn Cain,
Aleksander Kubica,
Sheng-Tao Wang,
Mikhail D. Lukin
Abstract:
Neutral atom arrays have recently emerged as a promising platform for fault-tolerant quantum computing. Based on these advances, including dynamically-reconfigurable connectivity and fast transversal operations, we present a low-overhead architecture that supports the layout and resource estimation of large-scale fault-tolerant quantum algorithms. Utilizing recent advances in fault tolerance with…
▽ More
Neutral atom arrays have recently emerged as a promising platform for fault-tolerant quantum computing. Based on these advances, including dynamically-reconfigurable connectivity and fast transversal operations, we present a low-overhead architecture that supports the layout and resource estimation of large-scale fault-tolerant quantum algorithms. Utilizing recent advances in fault tolerance with transversal gate operations, this architecture achieves a run time speed-up on the order of the code distance $d$, which we find directly translates to run time improvements of large-scale quantum algorithms. Our architecture consists of functional building blocks of key algorithmic subroutines, including magic state factories, quantum arithmetic units, and quantum look-up tables. These building blocks are implemented using efficient transversal operations, and we design space-time efficient versions of them that minimize interaction distance, thereby reducing atom move times and minimizing the volume for correlated decoding. We further propose models to estimate their logical error performance. We perform resource estimation for a large-scale implementation of Shor's factoring algorithm, one of the prototypical benchmarks for large-scale quantum algorithms, finding that 2048-bit RSA factoring can be executed with 19 million qubits in 5.6 days, for 1 ms QEC cycle times. This represents close to 50$\times$ speed-up of the run-time compared to existing estimates with similar assumptions, with no increase in space footprint.
△ Less
Submitted 21 May, 2025;
originally announced May 2025.
-
Fast correlated decoding of transversal logical algorithms
Authors:
Madelyn Cain,
Dolev Bluvstein,
Chen Zhao,
Shouzhen Gu,
Nishad Maskara,
Marcin Kalinowski,
Alexandra A. Geim,
Aleksander Kubica,
Mikhail D. Lukin,
Hengyun Zhou
Abstract:
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number of syndrome extraction rounds can be reduced by a factor of the code distance $d$, at the cost of increased classical decoding complexity. Here, we reformulate t…
▽ More
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number of syndrome extraction rounds can be reduced by a factor of the code distance $d$, at the cost of increased classical decoding complexity. Here, we reformulate the problem of decoding transversal circuits by directly decoding relevant logical operator products as they propagate through the circuit. This procedure transforms the decoding task into one closely resembling that of a single-qubit memory propagating through time. The resulting approach leads to fast decoding and reduced problem size while maintaining high performance. Focusing on the surface code, we prove that this method enables fault-tolerant decoding with minimum-weight perfect matching, and benchmark its performance on example circuits including magic state distillation. We find that the threshold is comparable to that of a single-qubit memory, and that the total decoding run time can be, in fact, less than that of conventional lattice surgery. Our approach enables fast correlated decoding, providing a pathway to directly extend single-qubit QEC techniques to transversal algorithms.
△ Less
Submitted 20 June, 2025; v1 submitted 19 May, 2025;
originally announced May 2025.
-
Counterdiabatic Driving with Performance Guarantees
Authors:
Jernej Rudi Finžgar,
Simone Notarnicola,
Madelyn Cain,
Mikhail D. Lukin,
Dries Sels
Abstract:
Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations which do not have performance guarantees. We propose and analyze a non-variational, system-agnostic CD expansion method and analytically show that it converge…
▽ More
Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations which do not have performance guarantees. We propose and analyze a non-variational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.
△ Less
Submitted 31 October, 2025; v1 submitted 3 March, 2025;
originally announced March 2025.
-
Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms
Authors:
Gefen Baranes,
Madelyn Cain,
J. Pablo Bonilla Ataides,
Dolev Bluvstein,
Josiah Sinclair,
Vladan Vuletic,
Hengyun Zhou,
Mikhail D. Lukin
Abstract:
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder…
▽ More
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally-motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis, and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault tolerant quantum computation in systems with loss error detection.
△ Less
Submitted 25 January, 2026; v1 submitted 27 February, 2025;
originally announced February 2025.
-
Probing the Kitaev honeycomb model on a neutral-atom quantum computer
Authors:
Simon J. Evered,
Marcin Kalinowski,
Alexandra A. Geim,
Tom Manovitz,
Dolev Bluvstein,
Sophie H. Li,
Nishad Maskara,
Hengyun Zhou,
Sepehr Ebadi,
Muqing Xu,
Joseph Campo,
Madelyn Cain,
Stefan Ostermann,
Susanne F. Yelin,
Subir Sachdev,
Markus Greiner,
Vladan Vuletić,
Mikhail D. Lukin
Abstract:
Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly-correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, due to the non-local nature of fermions, such models are challenging to simulate with qubit de…
▽ More
Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly-correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, due to the non-local nature of fermions, such models are challenging to simulate with qubit devices. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays. We utilize a fermion-to-qubit mapping based on Kitaev's model on a honeycomb lattice, in which fermionic statistics are encoded using long-range entangled states. We prepare these states efficiently using measurement and feedforward, realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram and verify the non-Abelian spin liquid phase by evaluating an odd Chern number. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study dynamics of the Fermi-Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry, and high-energy physics.
△ Less
Submitted 6 October, 2025; v1 submitted 30 January, 2025;
originally announced January 2025.
-
Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits
Authors:
Katherine Van Kirk,
Christian Kokail,
Jonathan Kunjummen,
Hong-Ye Hu,
Yanting Teng,
Madelyn Cain,
Jacob Taylor,
Susanne F. Yelin,
Hannes Pichler,
Mikhail Lukin
Abstract:
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, ou…
▽ More
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.
△ Less
Submitted 25 December, 2024;
originally announced December 2024.
-
Experimental Demonstration of Logical Magic State Distillation
Authors:
Pedro Sales Rodriguez,
John M. Robinson,
Paul Niklas Jepsen,
Zhiyang He,
Casey Duckering,
Chen Zhao,
Kai-Hsin Wu,
Joseph Campo,
Kevin Bagnall,
Minho Kwon,
Thomas Karolyshyn,
Phillip Weinberg,
Madelyn Cain,
Simon J. Evered,
Alexandra A. Geim,
Marcin Kalinowski,
Sophie H. Li,
Tom Manovitz,
Jesse Amato-Grill,
James I. Basham,
Liane Bernstein,
Boris Braverman,
Alexei Bylinskii,
Adam Choukri,
Robert DeAngelo
, et al. (48 additional authors not shown)
Abstract:
Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and corrected, enabling substantial reduction in logical error rates. However, the set of logical operations that can be easily implemented on such encoded qubits is often c…
▽ More
Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and corrected, enabling substantial reduction in logical error rates. However, the set of logical operations that can be easily implemented on such encoded qubits is often constrained, necessitating the use of special resource states known as 'magic states' to implement universal, classically hard circuits. A key method to prepare high-fidelity magic states is to perform 'distillation', creating them from multiple lower fidelity inputs. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d=3 and d=5 color codes, observing improvements of the logical fidelity of the output magic states compared to the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation, and represent an important step towards large-scale logical quantum processors.
△ Less
Submitted 19 December, 2024;
originally announced December 2024.
-
Quantum adiabatic optimization with Rydberg arrays: localization phenomena and encoding strategies
Authors:
Lisa Bombieri,
Zhongda Zeng,
Roberto Tricarico,
Rui Lin,
Simone Notarnicola,
Madelyn Cain,
Mikhail D. Lukin,
Hannes Pichler
Abstract:
Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native constraints of quantum hardware, necessitating encoding strategies to map the original problem into a hardware-conformant form. While the classical overhead asso…
▽ More
Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native constraints of quantum hardware, necessitating encoding strategies to map the original problem into a hardware-conformant form. While the classical overhead associated with such mappings is easily quantifiable and typically polynomial in problem size, it is much harder to quantify their overhead on the quantum algorithm, e.g., the transformation of the adiabatic timescale. In this work, we address this challenge on the concrete example of the encoding scheme proposed in [Nguyen et al., PRX Quantum 4, 010316 (2023)], which is designed to map optimization problems on arbitrarily connected graphs into Rydberg atom arrays. We consider the fundamental building blocks underlying this encoding scheme and determine the scaling of the minimum gap with system size along adiabatic protocols. Even when the original problem is trivially solvable, we find that the encoded problem can exhibit an exponentially closing minimum gap. We show that this originates from a quantum coherent effect, which gives rise to an unfavorable localization of the ground-state wavefunction. On the QuEra Aquila neutral atom machine, we observe such localization and its effect on the success probability of finding the correct solution to the encoded optimization problem. Finally, we propose quantum-aware modifications of the encoding scheme that avoid this quantum bottleneck and lead to an exponential improvement in the adiabatic performance. This highlights the crucial importance of accounting for quantum effects when designing strategies to encode classical problems onto quantum platforms.
△ Less
Submitted 18 April, 2025; v1 submitted 7 November, 2024;
originally announced November 2024.
-
Strategies for running the QAOA at hundreds of qubits
Authors:
Brandon Augustino,
Madelyn Cain,
Edward Farhi,
Swati Gupta,
Sam Gutmann,
Daniel Ranard,
Eugene Tang,
Katherine Van Kirk
Abstract:
We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the standard QAOA with instance-independent "tree" parameters chosen in advance. These tree parameters are chosen to optimize the MaxCut expectation for large girth gr…
▽ More
We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the standard QAOA with instance-independent "tree" parameters chosen in advance. These tree parameters are chosen to optimize the MaxCut expectation for large girth graphs. We provide extensive numerical evidence supporting the performance guarantee for tree parameters conjectured in [Phys.Rev A 103:042612] and see that the approximation ratios obtained with tree parameters are typically well beyond the conjectured lower bounds, often comparable to performing a full optimization. This suggests that in practice, the QAOA can achieve near-optimal performance without the need for parameter optimization.
Next, we modify the warm-start QAOA of Tate et al. [Quantum 7:1121]. The starting state for the QAOA is now an optimized product state associated with a solution of the Goemans-Williamson (GW) algorithm. Surprisingly, the tree parameters continue to perform well for the warm-start QAOA. We find that for random 3-regular graphs with hundreds of vertices, the expected cut obtained by the warm-start QAOA at depth $p \gtrsim 3$ is comparable to that of the standard GW algorithm.
Our numerics on random instances do not provide general performance guarantees but do provide substantial evidence that there exists a regime of instance sizes in which the QAOA finds good solutions at low depth without the need for parameter optimization. For each instance studied, we classically compute the expected size of the QAOA distribution of cuts; producing the actual cuts requires running on a quantum computer.
△ Less
Submitted 3 October, 2024;
originally announced October 2024.
-
Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation
Authors:
Hengyun Zhou,
Chen Zhao,
Madelyn Cain,
Dolev Bluvstein,
Nishad Maskara,
Casey Duckering,
Hong-Ye Hu,
Sheng-Tao Wang,
Aleksander Kubica,
Mikhail D. Lukin
Abstract:
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low logical error rates. However, for many practical quantum error correcting (QEC) codes such as the surface code, due to syndrome measurement errors, standard construc…
▽ More
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low logical error rates. However, for many practical quantum error correcting (QEC) codes such as the surface code, due to syndrome measurement errors, standard constructions require multiple extraction rounds -- on the order of the code distance $d$ -- for fault-tolerant computation, particularly considering fault-tolerant state preparation. Here, we show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds for a broad class of QEC codes, including the surface code with magic state inputs and feed-forward, to achieve ``transversal algorithmic fault tolerance". Through the combination of transversal operations and novel strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal logical measurement distribution can be made exponentially small in the distance, even if the instantaneous quantum state cannot be made close to a logical codeword due to measurement errors. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space-time cost of practical fault-tolerant quantum computation by over an order of magnitude.
△ Less
Submitted 4 August, 2025; v1 submitted 25 June, 2024;
originally announced June 2024.
-
Quantum quench dynamics as a shortcut to adiabaticity
Authors:
Alexander Lukin,
Benjamin F. Schiffer,
Boris Braverman,
Sergio H. Cantu,
Florian Huber,
Alexei Bylinskii,
Jesse Amato-Grill,
Nishad Maskara,
Madelyn Cain,
Dominik S. Wild,
Rhine Samajdar,
Mikhail D. Lukin
Abstract:
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation and realizations of adiabatic quantum algorithms in large systems, particularly when the adiabatic gap vanishes exponentially with system size. Using QuEra's Aqu…
▽ More
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation and realizations of adiabatic quantum algorithms in large systems, particularly when the adiabatic gap vanishes exponentially with system size. Using QuEra's Aquila programmable quantum simulator based on Rydberg atom arrays, we experimentally demonstrate a method to circumvent such limitations. Specifically, we develop and test a "sweep-quench-sweep" quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. These quenches introduce a macroscopic reconfiguration between states separated by an extensively large Hamming distance, akin to quantum many-body scars. Our experiments show that this approach significantly outperforms the adiabatic algorithm, illustrating that such quantum quench algorithms can provide a shortcut to adiabaticity for large-scale many-body quantum systems.
△ Less
Submitted 31 May, 2024;
originally announced May 2024.
-
Fault-tolerant compiling of classically hard IQP circuits on hypercubes
Authors:
Dominik Hangleiter,
Marcin Kalinowski,
Dolev Bluvstein,
Madelyn Cain,
Nishad Maskara,
Xun Gao,
Aleksander Kubica,
Mikhail D. Lukin,
Michael J. Gullans
Abstract:
Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic algorithms. Here, we develop and analyze a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits. We co-design the circuits with the appro…
▽ More
Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic algorithms. Here, we develop and analyze a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits. We co-design the circuits with the appropriate quantum error correcting codes for efficient implementation in a reconfigurable neutral atom array architecture, constituting what we call a fault-tolerant compilation of the sampling algorithm. Specifically, we consider a family of $[[2^D , D, 2]]$ quantum error detecting codes whose transversal and permutation gate set can realize arbitrary degree-$D$ instantaneous quantum polynomial (IQP) circuits. Using native operations of the code and the atom array hardware, we compile a fault-tolerant and fast-scrambling family of such IQP circuits in a hypercube geometry, realized recently in the experiments by Bluvstein et al. [Nature 626, 7997 (2024)]. We develop a theory of second-moment properties of degree-$D$ IQP circuits for analyzing hardness and verification of random sampling by mapping to a statistical mechanics model. We provide evidence that sampling from hypercube IQP circuits is classically hard to simulate and analyze the linear cross-entropy benchmark (XEB) in comparison to the average fidelity. To realize a fully scalable approach, we first show that Bell sampling from degree-$4$ IQP circuits is classically intractable and can be efficiently validated. We further devise new families of $[[O(d^D),D,d]]$ color codes of increasing distance $d$, permitting exponential error suppression for transversal IQP sampling. Our results highlight fault-tolerant compiling as a powerful tool in co-designing algorithms with specific error-correcting codes and realistic hardware.
△ Less
Submitted 7 March, 2025; v1 submitted 29 April, 2024;
originally announced April 2024.
-
Correlated decoding of logical algorithms with transversal gates
Authors:
Madelyn Cain,
Chen Zhao,
Hengyun Zhou,
Nadine Meister,
J. Pablo Bonilla Ataides,
Arthur Jaffe,
Dolev Bluvstein,
Mikhail D. Lukin
Abstract:
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation of logical qubits using transversal gates (Bluvstein et al., Nature 626, 58-65 (2024)), we show that the performance of logical algorithms can be substantially i…
▽ More
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation of logical qubits using transversal gates (Bluvstein et al., Nature 626, 58-65 (2024)), we show that the performance of logical algorithms can be substantially improved by decoding the qubits jointly to account for error propagation during transversal entangling gates. We find that such correlated decoding improves the performance of both Clifford and non-Clifford transversal entangling gates, and explore two decoders offering different computational runtimes and accuracies. In particular, by leveraging the deterministic propagation of stabilizer measurement errors through transversal Clifford gates, we find that correlated decoding enables the number of noisy syndrome extraction rounds between these gates to be reduced from $O(d)$ to $O(1)$ in Clifford circuits, where $d$ is the code distance. We verify numerically that this approach substantially reduces the space-time cost of deep logical Clifford circuits. These results demonstrate that correlated decoding provides a major advantage in early fault-tolerant computation, as realized in recent experiments, and further indicate it has considerable potential to reduce the space-time cost in large-scale logical algorithms.
△ Less
Submitted 7 April, 2025; v1 submitted 5 March, 2024;
originally announced March 2024.
-
Logical quantum processor based on reconfigurable atom arrays
Authors:
Dolev Bluvstein,
Simon J. Evered,
Alexandra A. Geim,
Sophie H. Li,
Hengyun Zhou,
Tom Manovitz,
Sepehr Ebadi,
Madelyn Cain,
Marcin Kalinowski,
Dominik Hangleiter,
J. Pablo Bonilla Ataides,
Nishad Maskara,
Iris Cong,
Xun Gao,
Pedro Sales Rodriguez,
Thomas Karolyshyn,
Giulia Semeghini,
Michael J. Gullans,
Markus Greiner,
Vladan Vuletic,
Mikhail D. Lukin
Abstract:
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a pro…
▽ More
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Utilizing logical-level control and a zoned architecture in reconfigurable neutral atom arrays, our system combines high two-qubit gate fidelities, arbitrary connectivity, as well as fully programmable single-qubit rotations and mid-circuit readout. Operating this logical processor with various types of encodings, we demonstrate improvement of a two-qubit logic gate by scaling surface code distance from d=3 to d=7, preparation of color code qubits with break-even fidelities, fault-tolerant creation of logical GHZ states and feedforward entanglement teleportation, as well as operation of 40 color code qubits. Finally, using three-dimensional [[8,3,2]] code blocks, we realize computationally complex sampling circuits with up to 48 logical qubits entangled with hypercube connectivity with 228 logical two-qubit gates and 48 logical CCZ gates. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling. These results herald the advent of early error-corrected quantum computation and chart a path toward large-scale logical processors.
△ Less
Submitted 6 December, 2023;
originally announced December 2023.
-
Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization
Authors:
Benjamin F. Schiffer,
Dominik S. Wild,
Nishad Maskara,
Madelyn Cain,
Mikhail D. Lukin,
Rhine Samajdar
Abstract:
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the evolution. Here, we consider the maximum independent set problem, which can be efficiently encoded in the Hamiltonian describing a Rydberg atom array. We present a gener…
▽ More
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the evolution. Here, we consider the maximum independent set problem, which can be efficiently encoded in the Hamiltonian describing a Rydberg atom array. We present a general construction of instances of the problem for which the minimum gap decays superexponentially with system size, implying a superexponentially large time to solution via adiabatic evolution. The small gap arises from locally independent choices, which cause the system to initially evolve and localize into a configuration far from the solution in terms of Hamming distance. We investigate remedies to this problem. Specifically, we show that quantum quenches in these models can exhibit signatures of quantum many-body scars, which in turn, can circumvent the superexponential gaps. By quenching from a suboptimal configuration, states with a larger ground state overlap can be prepared, illustrating the utility of quantum quenches as an algorithmic tool.
△ Less
Submitted 22 June, 2023;
originally announced June 2023.
-
Quantum speedup for combinatorial optimization with flat energy landscapes
Authors:
Madelyn Cain,
Sambuddha Chattopadhyay,
Jin-Guo Liu,
Rhine Samajdar,
Hannes Pichler,
Mikhail D. Lukin
Abstract:
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum Independent Set problem on certain unit-disk graph instances [Ebadi et al., Science 376, 6598 (2022)], we develop a theoretical framework to analyze the relative performa…
▽ More
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum Independent Set problem on certain unit-disk graph instances [Ebadi et al., Science 376, 6598 (2022)], we develop a theoretical framework to analyze the relative performance of the optimized quantum adiabatic algorithm and a broad class of classical Markov chain Monte Carlo algorithms. We outline conditions for the quantum adiabatic algorithm to achieve a quadratic speedup on hard problem instances featuring flat low-energy landscapes and provide example instances with either a quantum speedup or slowdown. We then introduce an additional local Hamiltonian with no sign problem to the optimized adiabatic algorithm to achieve a quadratic speedup over a wide class of classical simulated annealing, parallel tempering, and quantum Monte Carlo algorithms in solving these hard problem instances. Finally, we use this framework to analyze the experimental observations.
△ Less
Submitted 7 July, 2023; v1 submitted 22 June, 2023;
originally announced June 2023.
-
The QAOA gets stuck starting from a good classical string
Authors:
Madelyn Cain,
Edward Farhi,
Sam Gutmann,
Daniel Ranard,
Eugene Tang
Abstract:
The Quantum Approximate Optimization Algorithm (QAOA) is designed to maximize a cost function over bit strings. While the initial state is traditionally a uniform superposition over all strings, it is natural to try expediting the QAOA: first use a classical algorithm to produce some good string, and then run the standard QAOA starting in the computational basis state associated with that string.…
▽ More
The Quantum Approximate Optimization Algorithm (QAOA) is designed to maximize a cost function over bit strings. While the initial state is traditionally a uniform superposition over all strings, it is natural to try expediting the QAOA: first use a classical algorithm to produce some good string, and then run the standard QAOA starting in the computational basis state associated with that string. Here we report numerical experiments that show this method of initializing the QAOA fails dramatically, exhibiting little to no improvement of the cost function. We provide multiple analytical arguments for this lack of improvement, each of which can be made rigorous under different regimes or assumptions, including at nearly linear depths. We emphasize that our negative results only apply to our simple incarnation of the warm-start QAOA and may not apply to other approaches in the literature. We hope that our theoretical analysis will inform future algorithm design.
△ Less
Submitted 7 July, 2023; v1 submitted 11 July, 2022;
originally announced July 2022.
-
Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models
Authors:
Aarohi Srivastava,
Abhinav Rastogi,
Abhishek Rao,
Abu Awal Md Shoeb,
Abubakar Abid,
Adam Fisch,
Adam R. Brown,
Adam Santoro,
Aditya Gupta,
Adrià Garriga-Alonso,
Agnieszka Kluska,
Aitor Lewkowycz,
Akshat Agarwal,
Alethea Power,
Alex Ray,
Alex Warstadt,
Alexander W. Kocurek,
Ali Safaya,
Ali Tazarv,
Alice Xiang,
Alicia Parrish,
Allen Nie,
Aman Hussain,
Amanda Askell,
Amanda Dsouza
, et al. (426 additional authors not shown)
Abstract:
Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-futur…
▽ More
Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.
△ Less
Submitted 12 June, 2023; v1 submitted 9 June, 2022;
originally announced June 2022.
-
Computing solution space properties of combinatorial optimization problems via generic tensor networks
Authors:
Jin-Guo Liu,
Xun Gao,
Madelyn Cain,
Mikhail D. Lukin,
Sheng-Tao Wang
Abstract:
We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the independent set problem as an example, we show how all these solution space properties…
▽ More
We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the independent set problem as an example, we show how all these solution space properties can be computed in the unified approach of generic tensor networks. We demonstrate the versatility of this computational tool by applying it to several examples, including computing the entropy constant for hardcore lattice gases, studying the overlap gap properties, and analyzing the performance of quantum and classical algorithms for finding maximum independent sets.
△ Less
Submitted 23 September, 2022; v1 submitted 7 May, 2022;
originally announced May 2022.
-
Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
Authors:
Sepehr Ebadi,
Alexander Keesling,
Madelyn Cain,
Tout T. Wang,
Harry Levine,
Dolev Bluvstein,
Giulia Semeghini,
Ahmed Omran,
Jinguo Liu,
Rhine Samajdar,
Xiu-Zhe Luo,
Beatrice Nash,
Xun Gao,
Boaz Barak,
Edward Farhi,
Subir Sachdev,
Nathan Gemelke,
Leo Zhou,
Soonwon Choi,
Hannes Pichler,
Shengtao Wang,
Markus Greiner,
Vladan Vuletic,
Mikhail D. Lukin
Abstract:
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop…
▽ More
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
△ Less
Submitted 18 February, 2022;
originally announced February 2022.
-
The R-Process Alliance: J1521-3538, a very metal-poor, extremely r-process-enhanced star with [Eu/Fe]=+2.2, and the class of r-III stars
Authors:
Madelyn Cain,
Anna Frebel,
Alexander P. Ji,
Vinicius M. Placco,
Rana Ezzeddine,
Ian U. Roederer,
Kohei Hattori,
Timothy C. Beers,
Jorge Mélendez,
Terese T. Hansen,
Charli M. Sakari
Abstract:
We report the discovery of J1521-3538, a bright (V=12.2), very metal-poor ([Fe/H]=-2.8) strongly r-process enhanced field horizontal branch star, based on a high-resolution, high signal-to-noise Magellan/MIKE spectrum. J1521-3538 shows the largest r-process element over-abundance in any known r-process-enhanced star, with [Eu/Fe]=+2.2, and its chemical abundances of 22 neutron-capture elements clo…
▽ More
We report the discovery of J1521-3538, a bright (V=12.2), very metal-poor ([Fe/H]=-2.8) strongly r-process enhanced field horizontal branch star, based on a high-resolution, high signal-to-noise Magellan/MIKE spectrum. J1521-3538 shows the largest r-process element over-abundance in any known r-process-enhanced star, with [Eu/Fe]=+2.2, and its chemical abundances of 22 neutron-capture elements closely match the scaled solar r-process pattern. J1521-3538 is also one of few known carbon-enhanced metal-poor stars with r-process enhancement (CEMP-r stars), as found after correcting the measured C abundance for the star's evolutionary status. We propose to extend the existing classification of moderately enhanced (+0.3<=[Eu/Fe]<=+1.0) r-I and strongly r-process enhanced ([Eu/Fe]>+1.0) r-II stars to include an r-III class, for r-process stars such as J1521-3538, with [Eu/Fe]>+2.0 and [Ba/Eu]<-0.5, or >100 times the solar ratio of europium to iron. Using cosmochronometry, we estimate J1521-3538 to be 12.5+-5 Gyr and 8.9+-5 Gyr old, using two different sets of initial production ratios. These ages are based on measurements of the Th line at 4019 A and other r-process element abundances. This is broadly consistent with the old age of a low-mass metal-poor field red horizontal branch star. J1521-3538 likely originated in a low-mass dwarf galaxy that was later accreted by the Milky Way, as evidenced by its highly eccentric orbit.
△ Less
Submitted 14 June, 2020;
originally announced June 2020.
-
Inventory Loops (i.e. Counting Sequences) have Pre-period $2\max S_1+60$
Authors:
Onno M. Cain,
Sela T. Enin
Abstract:
An Inventory Sequence $(S_0, S_1, S_2, ...)$ is the iteration of the map $f$ defined roughly by taking an integer to its numericized description (e.g. $f(1381)=211318$ since "$1381$" has two $1$'s, one $3$, and one $8$). Our work analyzes the iteration under the infinite base. Any starting value of positive digits is known to be ultimately periodic [1] (e.g. $S_0=1381$ reaches the 1-cycle…
▽ More
An Inventory Sequence $(S_0, S_1, S_2, ...)$ is the iteration of the map $f$ defined roughly by taking an integer to its numericized description (e.g. $f(1381)=211318$ since "$1381$" has two $1$'s, one $3$, and one $8$). Our work analyzes the iteration under the infinite base. Any starting value of positive digits is known to be ultimately periodic [1] (e.g. $S_0=1381$ reaches the 1-cycle $f(3122331418)=3122331418$). Parametrizations of all possible cycles are also known [2,3]. We answer Bronstein and Fraenkel's open question of 26 years showing the pre-period of any such starting value is no more than $2M+60$ where $M=\max S_1$. And oddly the period of the cycle can be determined after only $O(\log\log M)$ iterations.
△ Less
Submitted 31 March, 2020;
originally announced April 2020.
-
Inelastic neutron scattering study of the anisotropic $S = 1$ spin chain [Ni(HF$_2$)(3-Clpyridine)$_4$]BF$_4$
Authors:
Daniel M. Pajerowski,
Jamie L. Manson,
Jacek Herbrych,
Jesper Bendix,
Andrey P. Podlesnyak,
John M. Cain,
Mark W. Meisel
Abstract:
[Ni(HF$_2$)(3-Clpyridine)$_4$]BF$_4$ (NBCT) is a one-dimensional, $S = 1$ spin chain material that shows no magnetic neutron Bragg peaks down temperatures of 0.1 K. Previous work identified NBCT to be in the Haldane phase and near a quantum phase transition as a function of $D/J$ to the large-$D$ quantum paramagnet phase (QPM), where $D$ is the axial single-ion anisotropy and $J$ is the intrachain…
▽ More
[Ni(HF$_2$)(3-Clpyridine)$_4$]BF$_4$ (NBCT) is a one-dimensional, $S = 1$ spin chain material that shows no magnetic neutron Bragg peaks down temperatures of 0.1 K. Previous work identified NBCT to be in the Haldane phase and near a quantum phase transition as a function of $D/J$ to the large-$D$ quantum paramagnet phase (QPM), where $D$ is the axial single-ion anisotropy and $J$ is the intrachain superexchange. Herein, inelastic neutron scattering results are presented on partially deuterated, $^{11}$B enriched NBCT polycrystalline samples in zero magnetic field and down to temperatures of 0.3 K. Comparison to density matrix renormalization group calculations yields $D/J = 1.51$ and a significant rhombic single-ion anisotropy $E$ ($E/D \approx 0.03$, $E/J \approx 0.05$). These $D$, $J$, and $E$ values place NBCT in the large-$D$ QPM phase but precipitously near a quantum phase transition to a long-range ordered phase.
△ Less
Submitted 23 January, 2020;
originally announced January 2020.
-
Prime-bounded subwords
Authors:
Onno M. Cain
Abstract:
In the number $373$ all subwords ($3$, $7$, $37$, $73$, and $373$) are prime. Similarly, in $9719$ all subwords are divisible by at most one prime. And similarly again in $7319797913$ all subwords are divisible by at most two primes. These are the largest integers with their respective properties. We show for any $k\ge 1$ there are only finitely many integers having subwords divisible by at most…
▽ More
In the number $373$ all subwords ($3$, $7$, $37$, $73$, and $373$) are prime. Similarly, in $9719$ all subwords are divisible by at most one prime. And similarly again in $7319797913$ all subwords are divisible by at most two primes. These are the largest integers with their respective properties. We show for any $k\ge 1$ there are only finitely many integers having subwords divisible by at most $k$ primes. In fact, we show for any $B$ and $d$ coprime that $n$ contains a base-$B$ subword divisible by $d$ if $n>B^d$. So as example consequence, past a certain point every prime contains a subword divisible by say $10000000007$.
△ Less
Submitted 15 December, 2019;
originally announced December 2019.
-
The Exceptional Selfcondensability of Powers of Five
Authors:
O. M. Cain
Abstract:
We show any power of five may be expressed arithmetically with the digits of its decimal representation. We also show powers of five (in decimal) contain any amount of zeros in a row.
We show any power of five may be expressed arithmetically with the digits of its decimal representation. We also show powers of five (in decimal) contain any amount of zeros in a row.
△ Less
Submitted 28 October, 2019;
originally announced October 2019.
-
Bioperational Multisets in Various Semi-rings
Authors:
Onno M. Cain
Abstract:
One can find lists of whole numbers having equal sum and product. We call such a creature a bioperational multiset. No one seems to have seriously studied them in areas outside whole numbers such as the rationals, Gaussian integers, or semi-rings. We enumerate all possible sum-products for a bioperational multiset over whole numbers and six additional domains.
One can find lists of whole numbers having equal sum and product. We call such a creature a bioperational multiset. No one seems to have seriously studied them in areas outside whole numbers such as the rationals, Gaussian integers, or semi-rings. We enumerate all possible sum-products for a bioperational multiset over whole numbers and six additional domains.
△ Less
Submitted 8 August, 2019;
originally announced August 2019.
-
The R-Process Alliance: Chemical Abundances for a Trio of R-Process-Enhanced Stars -- One Strong, One Moderate, One Mild
Authors:
Madelyn Cain,
Anna Frebel,
Maude Gull,
Alexander P. Ji,
Vinicius M. Placco,
Timothy C. Beers,
Jorge Melendez,
Rana Ezzeddine,
Andrew R. Casey,
Terese T. Hansen,
Ian U. Roederer,
Charli Sakari
Abstract:
We present detailed chemical abundances of three new bright (V ~ 11), extremely metal-poor ([Fe/H] ~ -3.0), r-process-enhanced halo red giants based on high-resolution, high-S/N Magellan/MIKE spectra. We measured abundances for 20-25 neutron-capture elements in each of our stars. J1432-4125 is among the most r-process rich r-II stars, with [Eu/Fe]= +1.44+-0.11. J2005-3057 is an r-I star with [Eu/F…
▽ More
We present detailed chemical abundances of three new bright (V ~ 11), extremely metal-poor ([Fe/H] ~ -3.0), r-process-enhanced halo red giants based on high-resolution, high-S/N Magellan/MIKE spectra. We measured abundances for 20-25 neutron-capture elements in each of our stars. J1432-4125 is among the most r-process rich r-II stars, with [Eu/Fe]= +1.44+-0.11. J2005-3057 is an r-I star with [Eu/Fe] = +0.94+-0.07. J0858-0809 has [Eu/Fe] = +0.23+-0.05 and exhibits a carbon abundance corrected for evolutionary status of [C/Fe]_corr = +0.76, thus adding to the small number of known carbon-enhanced r-process stars. All three stars show remarkable agreement with the scaled solar r-process pattern for elements above Ba, consistent with enrichment of the birth gas cloud by a neutron star merger. The abundances for Sr, Y, and Zr, however, deviate from the scaled solar pattern. This indicates that more than one distinct r-process site might be responsible for the observed neutron-capture element abundance pattern. Thorium was detected in J1432-4125 and J2005-3057. Age estimates for J1432-4125 and J2005-3057 were adopted from one of two sets of initial production ratios each by assuming the stars are old. This yielded individual ages of 12+-6 Gyr and 10+-6 Gyr, respectively.
△ Less
Submitted 10 July, 2018;
originally announced July 2018.
-
The R-Process Alliance: Discovery of the first metal-poor star with a combined r- and s-process element signature
Authors:
Maude Gull,
Anna Frebel,
Madelyn G. Cain,
Vinicius M. Placco,
Alexander P. Ji,
Carlo Abate,
Rana Ezzeddine,
Amanda I. Karakas,
Terese T. Hansen,
Charli Sakari,
Erika M. Holmbeck,
Rafael M. Santucci,
Andrew R. Casey,
Timothy C. Beers
Abstract:
We present a high-resolution (R~35,000), high signal-to-noise (S/N>200) Magellan/MIKE spectrum of the star RAVE J094921.8-161722, a bright (V=11.3) metal-poor red giant star with [Fe/H] = -2.2, identified as a carbon-enhanced metal-poor (CEMP) star from the RAVE survey. We report its detailed chemical abundance signature of light fusion elements and heavy neutron-capture elements. We find J0949-16…
▽ More
We present a high-resolution (R~35,000), high signal-to-noise (S/N>200) Magellan/MIKE spectrum of the star RAVE J094921.8-161722, a bright (V=11.3) metal-poor red giant star with [Fe/H] = -2.2, identified as a carbon-enhanced metal-poor (CEMP) star from the RAVE survey. We report its detailed chemical abundance signature of light fusion elements and heavy neutron-capture elements. We find J0949-1617 to be a CEMP star with s-process enhancement that must have formed from gas enriched by a prior r-process event. Light neutron-capture elements follow a low-metallicity s-process pattern, while the heavier neutron-capture elements above Eu follow an r-process pattern. The Pb abundance is high, in line with an s-process origin. Thorium is also detected, as expected from an r-process origin, as Th is not produced in the s-process. We employ nucleosynthesis model predictions that take an initial r-process enhancement into account, and then determine the mass transfer of carbon and s-process material from a putative more massive companion onto the observed star. The resulting abundances agree well with the observed pattern. We conclude that J0949-1617 is the first bonafide CEMP-r+s star identified. This class of objects has previously been suggested to explain stars with neutron-capture element patterns that originate from neither the r- or s-process alone. We speculate that J0949-1617 formed in an environment similar to those of ultra-faint dwarf galaxies like Tucana III and Reticulum II, which were enriched in r-process elements by one or multiple neutron star mergers at the earliest times.a
△ Less
Submitted 2 June, 2018;
originally announced June 2018.
-
Engineered spatial inversion symmetry breaking in an oxide heterostructure built from isosymmetric room-temperature magnetically ordered components
Authors:
J. Alaria,
P. Borisov,
M. S. Dyer,
T. D. Manning,
S. Lepadatu,
M. G. Cain,
E. D. Mishina,
N. E. Sherstyuk,
N. A. Ilyin,
J. Hadermann,
D. Lederman,
J. B. Claridge,
M. J. Rosseinsky
Abstract:
The oxide heterostructure [(YFeO$_3$)$_5$(LaFeO$_3$)$_5$]$_{40}$, which is magnetically ordered and piezoelectric at room temperature, has been constructed from two weak ferromagnetic AFeO$_3$ perovskites with different A cations using RHEED-monitored pulsed laser deposition. The polarisation arises through the removal of inversion centres present within the individual AFeO$_3$ components. This sy…
▽ More
The oxide heterostructure [(YFeO$_3$)$_5$(LaFeO$_3$)$_5$]$_{40}$, which is magnetically ordered and piezoelectric at room temperature, has been constructed from two weak ferromagnetic AFeO$_3$ perovskites with different A cations using RHEED-monitored pulsed laser deposition. The polarisation arises through the removal of inversion centres present within the individual AFeO$_3$ components. This symmetry reduction is a result of combining ordering on the A site, imposed by the periodicity of the grown structure, with appropriate orientations of the octahedral tilting characteristic of the perovskite units themselves, according to simple symmetry-controlled rules. The polarisation is robust against A site interdiffusion between the two layers which produces a sinusoidally modulated occupancy that retains the coupling of translational and point symmetries required to produce a polar structure. Magnetization and magneto-optical Kerr rotation measurements show that the heterostructure's magnetic structure is similar to that of the individual components. Evidence of the polarity was obtained from second harmonic generation and piezoelectric force microscopy measurements. Modeling of the piezoresponse allows extraction of $d_{33}$ (approximately 10 pC/N) of the heterostructure, which is in agreement with DFT calculations.
△ Less
Submitted 27 November, 2013;
originally announced November 2013.
-
Inferring Latent Structure From Mixed Real and Categorical Relational Data
Authors:
Esther Salazar,
Matthew Cain,
Elise Darling,
Stephen Mitroff,
Lawrence Carin
Abstract:
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix maps each row-column pair of binary feature vectors to an observed matrix element.…
▽ More
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix maps each row-column pair of binary feature vectors to an observed matrix element. The latent binary features of the rows are modeled via a multivariate Gaussian distribution with low-rank covariance matrix, and the Gaussian random variables are mapped to latent binary features via a probit link. The same type construction is applied jointly to the columns. The model infers latent, low-dimensional binary features associated with each row and each column, as well correlation structure between all rows and between all columns.
△ Less
Submitted 27 June, 2012;
originally announced June 2012.