Showing 1–37 of 37 results for author: Liu, D E

Branch-resolved Pauli-block spectroscopy of residual conditional phase in two-qubit gates

Authors: Xudan Chai, Yanwu Gu, Huiqi Xue, Kerui Li, Dong E. Liu

Abstract: Recent progress in quantum physics and quantum technologies is driving quantum computing from the noisy intermediate-scale (NISQ) era toward fault-tolerant operation. High-precision control of two-qubit gates is among the most critical requirements in this transition and hinges on accurate two-qubit calibration. For controlled-phase and CZ-style operations, the residual conditional phase (the nonl… ▽ More Recent progress in quantum physics and quantum technologies is driving quantum computing from the noisy intermediate-scale (NISQ) era toward fault-tolerant operation. High-precision control of two-qubit gates is among the most critical requirements in this transition and hinges on accurate two-qubit calibration. For controlled-phase and CZ-style operations, the residual conditional phase (the nonlocal ZZ-type deviation after local compensation) is weakly resolved at leading order in average infidelity and randomized benchmarking, and repeated Ramsey amplification does not reliably isolate it from ordinary target detuning, SPAM errors, and contrast loss in long sequences. We introduce branch-resolved Pauli-block spectroscopy to estimate the per-cycle residual ZZ-rotation angle theta_c with its sign, from which the controlled-phase residual follows by a fixed convention. The protocol repeats a fixed probe for N cycles, measures the closed Pauli block IX, IY, ZX, and ZY, and forms branch coherences C+ and C- conditioned on the control qubit; theta_c splits the two branch phase slopes in opposite directions, while local target phase beta_c shifts them together. An echoed-cycle variant suppresses removable local terms while preserving the nonlocal contribution. Numerical simulations with injected theta_c, detuning, damping, and SPAM confirm unbiased signed readout where scalar-sector alternatives fail and distinguish opposite-sign errors at equal infidelity. On one superconducting cloud qubit-coupler pair, a pulse-level calibration closed loop shows near-linear injection, preserved branch contrast, and tracking of the native residual conditional phase through one iteration. The approach yields a low-overhead, signed per-cycle estimate of residual conditional phase that standard fidelity benchmarks underresolve at leading order. △ Less

Submitted 15 July, 2026; v1 submitted 11 July, 2026; originally announced July 2026.

Möbius-Guided Diagonal-Gate Compilation with Native Multiqubit Controlled-Phase Gates on Neutral-Atom Processors

Authors: Hairuo Huang, Yanwu Gu, Chen Huang, Xi Zhao, Meng-Jun Hu, Dong E. Liu, Jingbo Wang

Abstract: Diagonal gates are ubiquitous primitives in quantum algorithms, from phase oracles, hypergraph-state preparation, and multi-control logic to Hamiltonian simulation of spin models and digitized lattice field theories, where Ising interactions and local potential terms are diagonal in the encoded basis. Standard compilers, however, often lower diagonal structure into one- and two-qubit gates before… ▽ More Diagonal gates are ubiquitous primitives in quantum algorithms, from phase oracles, hypergraph-state preparation, and multi-control logic to Hamiltonian simulation of spin models and digitized lattice field theories, where Ising interactions and local potential terms are diagonal in the encoded basis. Standard compilers, however, often lower diagonal structure into one- and two-qubit gates before neutral-atom hardware can exploit native Rydberg-mediated multiqubit controlled-phase operations. We propose a Möbius-guided compiler that maps a diagonal phase function to a phase hypergraph via subset-lattice Möbius inversion. The hypergraph retains the support and angle of each many-body phase term, allowing sparse or local high-order structure to be routed as native multiqubit controlled-phase candidates when feasible and decomposed otherwise. The neutral-atom scheduler accounts for atom motion, interaction-zone constraints, blockade feasibility, and error costs, enabling a direct comparison between native high-order execution and decomposed alternatives. Benchmarks against routed ZAP and ZX-calculus baselines show improved estimated success for algorithmic instances with exploitable three- and four-body phase terms, and comparable performance on predominantly two-body instances. These results provide a feasible compilation strategy for more fully exploiting the native capabilities of neutral-atom hardware, using atom reconfigurability and Rydberg-mediated multiqubit phase operations as practical resources for more efficient quantum computation. △ Less

Submitted 29 July, 2026; v1 submitted 9 July, 2026; originally announced July 2026.

Comments: 21 pages, 10 figures

Lazy-Move Compilation for Neutral-Atom Quantum Computers via a Buffer-Relay Fabric

Authors: Chen Huang, Jingbo Wang, Zhemin Zhang, Ming Zhong, Zhuo Fu, Zhiding Liang, Yuan Sun, Dong E. Liu

Abstract: Neutral atom quantum computing offers strong scalability and flexible qubit connectivity, but most existing compilation flows rely on reconfigurable atom arrays that physically shuttle qubit atoms during execution. Although this approach improves connectivity, it also introduces handoff errors, motional heating, and atom-loss risks that can degrade overall fidelity. We present BRIDGE, a Buffer-Rel… ▽ More Neutral atom quantum computing offers strong scalability and flexible qubit connectivity, but most existing compilation flows rely on reconfigurable atom arrays that physically shuttle qubit atoms during execution. Although this approach improves connectivity, it also introduces handoff errors, motional heating, and atom-loss risks that can degrade overall fidelity. We present BRIDGE, a Buffer-Relay Interconnect for Data-stable Gate Execution that co-designs a static, compiler-managed buffer-relay fabric with a lazy-move compiler that exploits it. BRIDGE targets an optimized, dual-species 2D interleaved atom array, using non-encoding ``buffer atoms'' to mediate long-range interactions in the fixed baseline and introducing limited data motion only for selected hotspots. By using calibrated heteronuclear and homonuclear Rydberg channels, BRIDGE realizes a static routing backbone in which data-buffer and buffer-buffer interactions are enabled while residual data-data crosstalk is suppressed. Across a 22-circuit matched benchmark suite re-estimated under a single shared error model, BRIDGE attains a geometric-mean $\sim$10$\times$ higher total fidelity than ZAP and $\sim$16$\times$ than Enola, together with $\sim$540$\times$ and $\sim$1000$\times$ lower circuit execution time, respectively, while reducing data-atom movement from thousands of transport events to zero. △ Less

Submitted 30 June, 2026; originally announced June 2026.

Comments: 18 pages, 17 figures

Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes

Authors: Yi Yuan, Yuanchen Zhao, Dong E. Liu

Abstract: Probabilistic error cancellation (PEC) is unbiased but suffers exponential sampling overhead set by noise-weighted circuit volume, whereas quantum error-detecting codes (QEDCs) remove many physical faults by stabilizer post-selection but leave an undetectable logical residue. We exploit this complementarity by using post-selection to map physical noise to a weaker accepted logical channel, and the… ▽ More Probabilistic error cancellation (PEC) is unbiased but suffers exponential sampling overhead set by noise-weighted circuit volume, whereas quantum error-detecting codes (QEDCs) remove many physical faults by stabilizer post-selection but leave an undetectable logical residue. We exploit this complementarity by using post-selection to map physical noise to a weaker accepted logical channel, and then applying PEC only to the residual channel. The resulting feedback-free QED+PEC scheme interleaves Clifford logical blocks, stabilizer measurements, post-selection, and probabilistic cancellation on accepted trajectories, without real-time decoding or active recovery. A key complication is that post-selection correlates accepted fault branches through stabilizer-commutation constraints, so the sparse Pauli-Lindblad factorization underlying bare PEC no longer applies directly. We therefore construct the inverse channel perturbatively: for fixed order $K$, only accepted fault branches up to order $K$ are retained, reducing preprocessing from $2^m$ branches to $O(m^K)$ per block. The order-$K$ protocol cancels the normalized post-selected channel through degree $K$, leaving a per-block error $O(W^{K+1})$ that accumulates at most linearly. For logical GHZ-state preparation with the $[[n,n-2,2]]$ Iceberg code under circuit-level depolarizing noise and ideal stabilizer measurements, first-order QED+PEC reaches $n=200$ physical qubits and lowers sampling overhead by three to four orders of magnitude relative to standard PEC while maintaining $F\simeq0.956$. Syndrome-noise tests show that readout-only flips mainly increase post-selection cost, whereas noisy GHZ-assisted global stabilizer extraction can remove the advantage. This identifies a discrete-Zeno trade-off: cheap detection reshapes the effective channel PEC must invert, rather than simply adding overhead. △ Less

Submitted 12 May, 2026; originally announced May 2026.

Comments: 33 pages, 13 figures

Topology-Aware Block Coordinate Descent for Qubit Frequency Allocation of Superconducting Quantum Processors

Authors: Zheng Zhao, Weifeng Zhuang, Yanwu Gu, Peng Qian, Xiao Xiao, Dong E. Liu

Abstract: Pre-execution calibration is a major bottleneck for operating superconducting quantum processors, and qubit frequency allocation is especially challenging due to crosstalk-coupled objectives. We establish that the widely-used Snake optimizer is mathematically equivalent to Block Coordinate Descent (BCD), providing a rigorous theoretical foundation for this strategy for qubit frequency allocation.… ▽ More Pre-execution calibration is a major bottleneck for operating superconducting quantum processors, and qubit frequency allocation is especially challenging due to crosstalk-coupled objectives. We establish that the widely-used Snake optimizer is mathematically equivalent to Block Coordinate Descent (BCD), providing a rigorous theoretical foundation for this strategy for qubit frequency allocation. Building on this formalization, we present a topology-aware block ordering obtained by casting order selection as a Sequence-Dependent Traveling Salesman Problem (SD-TSP) and solving it efficiently with a nearest-neighbor heuristic. The SD-TSP cost reflects how a given block choice expands the reduced-circuit footprint required to evaluate the block-local objective, enabling orders that minimize per-epoch evaluation time. Under local crosstalk/bounded-degree assumptions, the method achieves linear complexity in qubit count per epoch, while maintaining comparable optimization performance. We formalize the calibration objective, clarify when reduced experiments are equivalent or approximate to the full objective, and analyze convergence of the resulting inexact BCD with noisy measurements. Simulations based on a physics-motivated error simulator show that the proposed BCD-NNA ordering attains the same optimization accuracy at markedly lower runtime than graph-based heuristics (BFS, DFS) and random orders, while also achieving optimization quality comparable to a genetic-algorithm baseline. This method is robust to noisy objective-function evaluations and tolerant to moderate non-local crosstalk mismatch. These results provide a scalable, implementation-ready workflow for frequency calibration in near-term superconducting processors and, more broadly, for locality-structured calibration tasks in future scalable architectures. △ Less

Submitted 25 March, 2026; v1 submitted 15 January, 2026; originally announced January 2026.

Comments: 25 pages,6 figures

Journal ref: Quantum Sci. Technol. 11 035023 (2026)

Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout

Authors: Yuanchen Zhao, Li Rao, Dong E. Liu

Abstract: The preparation of long-range entangled (LRE) states via quantum measurements is a promising strategy, yet its stability against realistic, non-commuting measurement noise remains a critical open question. Here, we systematically investigate the rich phase structure emerging from a minimal model of competing, non-commuting weak measurements: nearest-neighbor Ising ($Z_iZ_j$) and single-qubit trans… ▽ More The preparation of long-range entangled (LRE) states via quantum measurements is a promising strategy, yet its stability against realistic, non-commuting measurement noise remains a critical open question. Here, we systematically investigate the rich phase structure emerging from a minimal model of competing, non-commuting weak measurements: nearest-neighbor Ising ($Z_iZ_j$) and single-qubit transverse ($X_i$) operators. We analyze three experimentally relevant scenarios based on which measurement outcomes are read out: complete readout, no readout, and partial readout. Using a replica mean-field theory for higher dimensions, complemented by numerical simulations in one dimension, we derive the complete finite-time and stationary phase diagrams. Our analysis reveals a striking dependence on the readout protocol. Complete readout yields a direct transition between a short-range entangled (SRE) phase and a pure LRE phase. No readout (pure decoherence) precludes entanglement but exhibits a strong-to-weak spontaneous symmetry breaking (SWSSB) transition into a classically ordered mixed state. Most intriguingly, partial readout interpolates between these limits, featuring a mixed-state phase transition where the system can become trapped in the SWSSB phase or, for weaker non-commutativity, undergo successive symmetry breaking to reach a mixed LRE phase. A novel technical contribution is the use of a channel-fidelity-based partition function that allows us to simultaneously characterize both entanglement and SWSSB order, revealing a deep interplay between them in the replica limit. These results provide a cohesive picture for understanding measurement phase transitions, SWSSB, and mixed-state phase transitions, offering crucial insights for designing robust state preparation protocols on noisy quantum devices. △ Less

Submitted 21 August, 2025; originally announced August 2025.

Comments: 38 pages, 4 figures

Journal ref: Phys. Rev. B 113, 174312 (2026)

Direct Nuclear-Level Qubits using Trapped Th-229 Ions: A Platform for Entanglement and Universal Quantum Information Processing

Authors: Jingbo Wang, Haixing Miao, Shiqian Ding, Dong E. Liu

Abstract: The low-energy isomeric transition in Thorium-229 offers a unique interface between nuclear and atomic physics, presenting a resource for quantum technologies that is notably resilient to environmental decoherence. While early experiments focused on nuclei in solid-state crystals, the recent advent of a continuous-wave vacuum ultraviolet laser at 148.4~nm now enables direct coherent control of ind… ▽ More The low-energy isomeric transition in Thorium-229 offers a unique interface between nuclear and atomic physics, presenting a resource for quantum technologies that is notably resilient to environmental decoherence. While early experiments focused on nuclei in solid-state crystals, the recent advent of a continuous-wave vacuum ultraviolet laser at 148.4~nm now enables direct coherent control of individual trapped Th-229 ions. Building on this breakthrough, we present a theoretical framework for utilizing trapped Th-229^{3+} ions as high-fidelity nuclear-level qubits, wherein quantum state preparation, single-qubit control, and entangling operations based on nuclear energy levels can all be efficiently realized. We analyze a scheme to generate entanglement between the nuclear isomeric states of two ions through phonon-mediated coupling, driven by optimized red- and blue-detuned laser sideband pulses. Our analysis, grounded in realistic experimental parameters, also demonstrates that high-fidelity entanglement is achievable, leveraging the nucleus's intrinsically long coherence times. These results provide a practical roadmap for developing nuclear-based quantum information processors and suggest that entangled nuclear-level qubits could potentially unlock new frontiers in precision metrology. △ Less

Submitted 14 August, 2025; originally announced August 2025.

Comments: 12 pages, 4 figures

Detecting entanglement with transport measurement in weakly interacting and fluctuating systems

Authors: Zhenhua Zhu, Gu Zhang, Dong E. Liu

Abstract: Measuring entanglement entropy in interacting, multipartite systems remains a significant experimental challenge. We address this challenge by developing a protocol to measure von Neumann entropy (VNE) and mutual information in quantum transport systems with both many-body interactions and multiple subsystems. Our analysis indicates that the vital connection between VNE and two-point correlation f… ▽ More Measuring entanglement entropy in interacting, multipartite systems remains a significant experimental challenge. We address this challenge by developing a protocol to measure von Neumann entropy (VNE) and mutual information in quantum transport systems with both many-body interactions and multiple subsystems. Our analysis indicates that the vital connection between VNE and two-point correlation functions persists under these realistic conditions. The measurement is shown to be feasible for systems with boundary interactions and, critically, for bulk-interacting systems subject to a quantum quench of their internal couplings. Our work provides a pathway to experimentally quantify entanglement in complex interacting systems and establishes mutual information as an experimentally accessible indicator for system-environment entanglement. △ Less

Submitted 4 August, 2025; originally announced August 2025.

Comments: 17 pages, 1 figure

Journal ref: Phys. Rev. B 113, 035447 (2026)

Protocol for detecting the nonlocality of the multi-Majorana Systems

Authors: Bai-Ting Liu, Peng Qian, Zhan Cao, Dong E. Liu

Abstract: Majorana zero modes (MZMs) are non-Abelian quasiparticles with the potential to serve as topological qubits for fault-tolerant quantum computing due to their ability to encode quantum information nonlocally. In multi-Majorana systems configured into two separated subsystems, nontrivial quantum correlations persist, but the presence of trivial Andreev bound states (ABSs) can obscure this nonlocalit… ▽ More Majorana zero modes (MZMs) are non-Abelian quasiparticles with the potential to serve as topological qubits for fault-tolerant quantum computing due to their ability to encode quantum information nonlocally. In multi-Majorana systems configured into two separated subsystems, nontrivial quantum correlations persist, but the presence of trivial Andreev bound states (ABSs) can obscure this nonlocality if MZM preparation fails. To address this, we propose a protocol using an entanglement witness based solely on parity measurements to distinguish the nonlocal characteristics of MZM systems. Our framework, which is experimentally implementable, achieves a detection probability of approximately 18% in a 6-site system and demonstrates robustness under environmental noise, albeit with a reduced detection rate in the resence of quasiparticle contamination. △ Less

Submitted 20 June, 2025; originally announced June 2025.

Hierarchical Quantum Optimization via Backbone-Driven Problem Decomposition: Integrating Tabu-Search with QAOA

Authors: Minhui Gou, Zeyang Li, Hong-Ze Xu, Changbin Lu, Jing-Bo Wang, Yukun Wang, Meng-Jun Hu, Dong E Liu, Wei-Feng Zhuang

Abstract: As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the scalability of QAOA for large-scale optimization tasks. To overcome these challenges, we propose Backbone-Driven QAOA, a hybrid framework that leverages adaptive… ▽ More As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the scalability of QAOA for large-scale optimization tasks. To overcome these challenges, we propose Backbone-Driven QAOA, a hybrid framework that leverages adaptive Tabu search for classical preprocessing to decompose large-scale quadratic unconstrained binary (QUBO) problems into NISQ-compatible subproblems. In our approach, adaptive Tabu search dynamically identifies and fixes backbone variables to construct reduced-dimensional subspaces that preserve the critical optimization landscape. These quantum-tractable subproblems are then solved via QAOA, with the resulting solutions iteratively refining the backbone selection in a closed-loop quantum-classical cycle. Experimental results demonstrate that our approach not only competes with, and in some cases surpasses, traditional classical algorithms but also performs comparably with recently proposed hybrid classical-quantum algorithms. Our proposed framework effectively orchestrates the allocation of quantum and classical resources, thereby enabling the solution of large-scale combinatorial optimization problems on current NISQ hardware. △ Less

Submitted 13 April, 2025; originally announced April 2025.

Comments: 10 pages, 6 figures

Fragility of Magic State Distillation under Imperfect Measurements

Authors: Yunzhe Zheng, Yuanchen Zhao, Dong E. Liu

Abstract: Magic state distillation (MSD) is the leading approach to generate the non-Clifford resources required for universal fault-tolerant quantum computation. While most analyses assume ideal measurements in the distillation process, this assumption breaks down on near-term hardware where measurement fidelity remains limited and large quantum error-correcting codes are unavailable. Here we establish a g… ▽ More Magic state distillation (MSD) is the leading approach to generate the non-Clifford resources required for universal fault-tolerant quantum computation. While most analyses assume ideal measurements in the distillation process, this assumption breaks down on near-term hardware where measurement fidelity remains limited and large quantum error-correcting codes are unavailable. Here we establish a general framework to analyze MSD under imperfect measurements, and reveal a sharp threshold phenomenon that differs from previous known threshold on input state error: Below a critical measurement strength, MSD loses its distillation power entirely, whereas above the threshold, the \textit{target states} are at most first-order biased and the \textit{distillation efficiency} is reduced to linear, leading to exponentially higher distillation overheads. To mitigate this fragility, we present a universal method to maximize MSD robustness against imperfect measurements by choosing stabilizer generators in standard form, which applies to all known protocols without incurring additional costs. Our work reveal fundamental constraints on MSD protocols with measurement noise and provide insights for designing practically robust distillation protocols in the near-term era of quantum hardware. △ Less

Submitted 13 January, 2026; v1 submitted 2 March, 2025; originally announced March 2025.

PPO-Q: Proximal Policy Optimization with Parametrized Quantum Policies or Values

Authors: Yu-Xin Jin, Zi-Wei Wang, Hong-Ze Xu, Wei-Feng Zhuang, Meng-Jun Hu, Dong E. Liu

Abstract: Quantum machine learning (QML), which combines quantum computing with machine learning, is widely believed to hold the potential to outperform traditional machine learning in the era of noisy intermediate-scale quantum (NISQ). As one of the most important types of QML, quantum reinforcement learning (QRL) with parameterized quantum circuits as agents has received extensive attention in the past fe… ▽ More Quantum machine learning (QML), which combines quantum computing with machine learning, is widely believed to hold the potential to outperform traditional machine learning in the era of noisy intermediate-scale quantum (NISQ). As one of the most important types of QML, quantum reinforcement learning (QRL) with parameterized quantum circuits as agents has received extensive attention in the past few years. Various algorithms and techniques have been introduced, demonstrating the effectiveness of QRL in solving some popular benchmark environments such as CartPole, FrozenLake, and MountainCar. However, tackling more complex environments with continuous action spaces and high-dimensional state spaces remains challenging within the existing QRL framework. Here we present PPO-Q, which, by integrating hybrid quantum-classical networks into the actor or critic part of the proximal policy optimization (PPO) algorithm, achieves state-of-the-art performance in a range of complex environments with significantly reduced training parameters. The hybrid quantum-classical networks in the PPO-Q incorporate two additional traditional neural networks to aid the parameterized quantum circuits in managing high-dimensional state encoding and action selection. When evaluated on 8 diverse environments, including four with continuous action space, the PPO-Q achieved comparable performance with the PPO algorithm but with significantly reduced training parameters. Especially, we accomplished the BipedalWalker environment, with a high-dimensional state and continuous action space simultaneously, which has not previously been reported in the QRL. More importantly, the PPO-Q is very friendly to the current NISQ hardware. We successfully trained two representative environments on the real superconducting quantum devices via the Quafu quantum cloud service. △ Less

Submitted 13 January, 2025; originally announced January 2025.

QSteed: A Resource-Virtualized and Hardware-Aware Quantum Compilation Framework for Real Quantum Computing Processors

Authors: Hong-Ze Xu, Zheng-An Wang, Yu-Long Feng, Yu Chen, Xinpeng Zhang, Jingbo Wang, Xu-Dan Chai, Wei-Feng Zhuang, Yu-Xin Jin, Yirong Jin, Haifeng Yu, Heng Fan, Meng-Jun Hu, Dong E. Liu

Abstract: As quantum computing systems continue to scale up and become more clustered, efficiently compiling user quantum programs into high fidelity executable sequences on real hardware remains a key challenge for current quantum compilation systems. In this study, we introduce a system software framework that integrates resource virtualization and hardware aware compilation for real quantum computing pro… ▽ More As quantum computing systems continue to scale up and become more clustered, efficiently compiling user quantum programs into high fidelity executable sequences on real hardware remains a key challenge for current quantum compilation systems. In this study, we introduce a system software framework that integrates resource virtualization and hardware aware compilation for real quantum computing processors, termed QSteed. QSteed virtualizes quantum processors through a four layer abstraction hierarchy comprising the Real Quantum Processing Unit (QPU), Standard QPU (StdQPU), Substructure of the QPU (SubQPU), and Virtual QPU (VQPU). These abstractions, together with calibration data, device topology, and noise descriptors, are maintained in a dedicated database to enable unified and fine grained management across superconducting quantum platforms. At run time, the modular compiler queries the database to match each incoming circuit with the most suitable VQPU, after which it confines layout, routing, gate resynthesis, and noise adaptive optimizations to that virtual subregion. The complete stack has been deployed on the Quafu superconducting cluster, where experimental runs confirm the correctness of the virtualization model and the efficacy of the compiler without requiring modifications to user code. By integrating resource virtualization with a select-then-compile workflow, QSteed demonstrates a robust architecture for compiling programs on noisy superconducting processors. This architectural approach offers a promising path towards efficient compilation needs across various superconducting quantum computing platforms in the noisy intermediate scale quantum (NISQ) era. △ Less

Submitted 20 January, 2026; v1 submitted 12 January, 2025; originally announced January 2025.

Comments: Full paper of QSteed, with 29 pages including appendices, 6 figures in the main text

Journal ref: Research 8, 0947 (2025)

From Magic State Distillation to Dynamical Systems

Authors: Yunzhe Zheng, Dong E. Liu

Abstract: Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes with transversal $T$ gates, there exists quite several protocols that don't fall into this class. Here we propose a method to map MSD protocols to iterative dynam… ▽ More Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes with transversal $T$ gates, there exists quite several protocols that don't fall into this class. Here we propose a method to map MSD protocols to iterative dynamical systems under the framework of stabilizer reduction. With the proposed mapping, we are able to analyze the performance of MSD protocols using techniques from dynamical systems theory, easily simulate the distillation process of input states under arbitrary noise and visualize it using flow diagram. We apply our mapping to common MSD protocols for $\ket{T}$ state and find some interesting properties: The $[[15, 1, 3]]$ code may distill states corresponding to $\sqrt{T}$ gate and the $[[5, 1, 3]]$ code can distill the magic state corresponding to the $T$ gate. Besides, we examine the exotic MSD protocols that may distill into other magic states proposed in [Eur. Phys. J. D 70, 55 (2016)] and identify the condition for distillable magic states. We also study new MSD protocols generated by concatenating different codes and numerically demonstrate that concatenation can generate MSD protocols with various magic states. By concatenating efficient codes with exotic codes, we can reduce the overhead of the exotic MSD protocols. We believe our proposed method will be a useful tool for simulating and visualization MSD protocols for canonical MSD protocols on $\ket{T}$ as well as other unexplored MSD protocols for other states. △ Less

Submitted 9 September, 2025; v1 submitted 5 December, 2024; originally announced December 2024.

Comments: to be appeared in Quantum

Journal ref: Quantum 9, 1858 (2025)

ZAP: Zoned Architecture and Performant Compiler for Field Programmable Atom Array

Authors: Chen Huang, Xi Zhao, Hongze Xu, Weifeng Zhuang, Meng-Jun Hu, Dong E. Liu, Jingbo Wang

Abstract: The scalability of neutral-atom quantum computing is increasingly limited by a compiler--architecture challenge: logical circuits must be mapped onto dynamically reconfigurable atom arrays while controlling crosstalk, transport overhead, and hardware constraints. To address this problem, we present ZAP, a co-designed zoned architecture and deterministic compiler for field-programmable atom arrays.… ▽ More The scalability of neutral-atom quantum computing is increasingly limited by a compiler--architecture challenge: logical circuits must be mapped onto dynamically reconfigurable atom arrays while controlling crosstalk, transport overhead, and hardware constraints. To address this problem, we present ZAP, a co-designed zoned architecture and deterministic compiler for field-programmable atom arrays. ZAP partitions the array into storage and entanglement zones and combines hardware-aware ASAP-separate scheduling, look-ahead placement, and conflict-aware routing in a single-pass compilation flow, thereby avoiding the repeated global search used in prior approaches. Evaluated on structured quantum benchmarks and random 3-regular circuits, ZAP consistently delivers multi-order-of-magnitude compilation speedups while maintaining competitive or superior execution quality. Relative to ZAC and PowerMove, ZAP typically reduces compilation time from tens of seconds to below 0.1~s and achieves speedups exceeding 1,000$\times$; relative to Enola, the speedup exceeds 10,000$\times$ on the evaluated suite. ZAP's fidelity gains are most pronounced on structured workloads with irregular connectivity and nonuniform qubit reuse, where its scheduling and placement decisions more effectively suppress crosstalk and limit transport-related loss, while on random circuits it remains competitive and preserves the same scalability advantage. These results show that hardware-structured, non-iterative compilation provides a practical path toward fast, scalable, and noise-aware neutral-atom quantum computing. △ Less

Submitted 22 May, 2026; v1 submitted 21 November, 2024; originally announced November 2024.

Journal ref: IEEE Transactions on Quantum Engineering, 2026

Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling

Authors: Rui-Cheng Guo, Yanwu Gu, Dong E. Liu

Abstract: Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital methods, such as lower systematic errors and reduced circuit depth, making them efficient for studying complex quantum phenomena. However, unlike their digital c… ▽ More Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital methods, such as lower systematic errors and reduced circuit depth, making them efficient for studying complex quantum phenomena. However, unlike their digital counterparts, analog quantum simulations face significant limitations due to the absence of effective error mitigation techniques. This work introduces two novel error mitigation strategies -- Hamiltonian reshaping and Hamiltonian rescaling -- in analog quantum simulation for tasks like eigen-energy evaluation. Hamiltonian reshaping uses random unitary transformations to generate new Hamiltonians with identical eigenvalues but varied eigenstates, allowing error reduction through averaging. Hamiltonian rescaling mitigates errors by comparing eigenvalue estimates from energy-scaled Hamiltonians. Numerical calculations validate both methods, demonstrating their significant practical effectiveness in enhancing the accuracy and reliability of analog quantum simulators. △ Less

Submitted 28 January, 2025; v1 submitted 31 October, 2024; originally announced October 2024.

Comments: Published version, 15 pages, 5 figures, 1 table. Supplementary Information is available on the journal's article page

Journal ref: npj Quantum Information 11, 14 (2025)

A Novel Quantum Realization of Jet Clustering in High-Energy Physics Experiments

Authors: Yongfeng Zhu, Weifeng Zhuang, Chen Qian, Yunheng Ma, Dong E. Liu, Manqi Ruan, Chen Zhou

Abstract: Exploring the application of quantum technologies to fundamental sciences holds the key to fostering innovation for both sides. In high-energy particle collisions, quarks and gluons are produced and immediately form collimated particle sprays known as jets. Accurate jet clustering is crucial as it retains the information of the originating quark or gluon and forms the basis for studying properties… ▽ More Exploring the application of quantum technologies to fundamental sciences holds the key to fostering innovation for both sides. In high-energy particle collisions, quarks and gluons are produced and immediately form collimated particle sprays known as jets. Accurate jet clustering is crucial as it retains the information of the originating quark or gluon and forms the basis for studying properties of the Higgs boson, which underlies teh mechanism of mass generation for subatomic particles. For the first time, by mapping collision events into graphs--with particles as nodes and their angular separations as edges--we realize jet clustering using the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical algorithm for addressing classical combinatorial optimization problems with available quantum resources. Our results, derived from 30 qubits on quantum computer simulator and 6 qubits on quantum computer hardware, demonstrate that jet clustering performance with QAOA is comparable with or even better than classical algorithms for a small-sized problem. This study highlights the feasibility of quantum computing to revolutionize jet clustering, bringing the practical application of quantum computing in high-energy physics experiments one step closer. △ Less

Submitted 7 June, 2025; v1 submitted 12 July, 2024; originally announced July 2024.

Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition

Authors: Yuanchen Zhao, Dong E. Liu

Abstract: The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we unravel their relations and propose a unified framework to extract an intrinsic error threshold from… ▽ More The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we unravel their relations and propose a unified framework to extract an intrinsic error threshold from the approximate QEC condition, which could upper bound other decoder-dependent error thresholds. Our proof establishes that relative entropy, effectively measuring deviations from exact QEC conditions, serves as the order parameter delineating the transition from asymptotic recoverability to unrecoverability. Consequently, we establish a unified framework for determining the error threshold across both exact and approximate QEC codes, addressing errors originating from noise channels as well as those from code space imperfections. This result sharpens our comprehension of error thresholds across diverse QEC codes and error models. △ Less

Submitted 13 January, 2025; v1 submitted 28 December, 2023; originally announced December 2023.

Comments: 20 pages, 2 figure

Journal ref: Phys. Rev. Research 6, 043258 (2024)

Mitigating crosstalk and residual coupling errors in superconducting quantum processors using many-body localization

Authors: Peng Qian, Hong-Ze Xu, Peng Zhao, Xiao Li, Dong E. Liu

Abstract: Addressing the paramount need for precise calibration in superconducting quantum qubits, especially in frequency control, this study introduces a novel calibration scheme harnessing the principles of Many-Body Localization (MBL). While existing strategies, such as Google's snake algorithm, have targeted optimization of qubit frequency parameters, our MBL-based methodology emerges as a stalwart aga… ▽ More Addressing the paramount need for precise calibration in superconducting quantum qubits, especially in frequency control, this study introduces a novel calibration scheme harnessing the principles of Many-Body Localization (MBL). While existing strategies, such as Google's snake algorithm, have targeted optimization of qubit frequency parameters, our MBL-based methodology emerges as a stalwart against noise, notably crosstalk and residual coupling errors, thereby significantly enhancing quantum processor fidelity and stability without necessitating extensive optimization computation. Not only does this approach provide a marked improvement in performance, particularly where specific residue couplings are present, but it also presents a more resource-efficient and cost-effective calibration process. The research delineated herein affords fresh insights into advanced calibration strategies and propels forward the domain of superconducting quantum computation by offering a robust framework for future explorations in minimizing error and optimizing qubit performance. △ Less

Submitted 15 October, 2023; v1 submitted 10 October, 2023; originally announced October 2023.

Comments: 8 pages, 4 figures, 1 table, with minor changes and reference list updated

Comparisons among the Performances of Randomized-framed Benchmarking Protocols under T1, T2 and Coherent Error Models

Authors: Xudan Chai, Yanwu Gu, Weifeng Zhuang, Peng Qian, Xiao Xiao, Dong E Liu

Abstract: While fundamental scientific researchers are eagerly anticipating the breakthroughs of quantum computing both in theory and technology, the current quantum computer, i.e. noisy intermediate-scale quantum (NISQ) computer encounters a bottleneck in how to deal with the noisy situation of the quantum machine. It is still urgently required to construct more efficient and reliable benchmarking protocol… ▽ More While fundamental scientific researchers are eagerly anticipating the breakthroughs of quantum computing both in theory and technology, the current quantum computer, i.e. noisy intermediate-scale quantum (NISQ) computer encounters a bottleneck in how to deal with the noisy situation of the quantum machine. It is still urgently required to construct more efficient and reliable benchmarking protocols through which one can assess the noise level of a quantum circuit that is designed for a quantum computing task. The existing methods that are mainly constructed based on a sequence of random circuits, such as randomized benchmarking (RB), have been commonly adopted as the conventional approach owning to its reasonable resource consumption and relatively acceptable reliability, compared with the average gate fidelity. To more deeply understand the performances of the above different randomized-framed benchmarking protocols, we design special random circuit sequences to test the performances of the three selected standard randomized-frame protocols under T1, T2, and coherent errors, which are regarded to be more practical for a superconductor quantum computer. The simulations indicate that MRB, DRB, and CRB sequentially overestimate the average error rate in the presence of T1 and T2 noise, compared with the conventional circuit's average error. Moreover, these methods exhibit almost the same level of sensitivity to the coherent error. Furthermore, the DRB loses its reliability when the strengths of T1 grow. More practically, the simulated conclusion is verified by running the designed tasks for three protocols on the Quafu quantum computation cloud platform. We find that MRB produces a more precise assessment of a quantum circuit conditioned on limited resources. However, the DRB provides a more stable estimation at a specific precision while a more resource-consuming. △ Less

Submitted 27 September, 2023; originally announced September 2023.

Work Statistics and Adiabatic Assumption in Nonequilibrium Many-Body Theory

Authors: Yi Zuo, Qinghong Yang, Bang-Gui Liu, Dong E Liu

Abstract: Keldysh field theory, based on adiabatic assumptions, serves as an widely used framework for addressing nonequilibrium many-body systems. Nonetheless, the validity of such adiabatic assumptions when addressing interacting Gibbs states remains a topic of contention. We use the knowledge of work statistics developed in nonequilibrium thermodynamics to study this problem. Consequently, we deduce a un… ▽ More Keldysh field theory, based on adiabatic assumptions, serves as an widely used framework for addressing nonequilibrium many-body systems. Nonetheless, the validity of such adiabatic assumptions when addressing interacting Gibbs states remains a topic of contention. We use the knowledge of work statistics developed in nonequilibrium thermodynamics to study this problem. Consequently, we deduce a universal theorem delineating the characteristics of evolutions that transition an initial Gibbs state to another. Based on this theorem, we analytically ascertain that adiabatic evolutions fail to transition a non-interacting Gibbs state to its interacting counterpart. However, this adiabatic approach remains a superior approximation relative to its non-adiabatic counterpart. Numerics verifying our theory and predictions are also provided. Furthermore, our findings render insights into the preparation of Gibbs states within the domain of quantum computation. △ Less

Submitted 21 September, 2023; v1 submitted 12 September, 2023; originally announced September 2023.

Comments: 5+7 pages, 2 figures. Supplementary information containing calculation details is presented. Expressions have been polished

Journal ref: Physical Review E 110 (2), L022105 (2023)

Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space

Authors: Yuanchen Zhao, Dong E. Liu

Abstract: Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we scrutinize the performance of the topological toric code in 2 dimension (2D) under the dual influence of stochastic noise and quantum deviations, especially during the… ▽ More Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we scrutinize the performance of the topological toric code in 2 dimension (2D) under the dual influence of stochastic noise and quantum deviations, especially during the critical phases of initial state preparation and error detection facilitated by multi-qubit entanglement gates. By mapping the protocol for multi-round error detection--from the inception of an imperfectly prepared code state via imperfect stabilizer measurements--to a statistical mechanical model characterized by a 3-dimensional $\mathbb{Z}_2$ gauge theory coupled with a 2-dimensional $\mathbb{Z}_2$ gauge theory, we establish a novel link between the error threshold and the model's phase transition point. We find two distinct error thresholds that demarcate varying efficacies in error correction. The empirical threshold that signifies the operational success of QEC aligns with the theoretical ideal of flawless state preparation operations. Contrarily, below another finite theoretical threshold, a phenomenon absent in purely stochastic error models emerges: unidentifiable measurement errors precipitate QEC failure in scenarios with large code distances. For codes of finite or modest distance $d$, it is revealed that maintaining the preparation error rate beneath a crossover scale, proportional to $1/\log d$, allows for the suppression of logical errors. Considering that fault-tolerant quantum computation is valuable only in systems with large scale and exceptionally low logical error rates, this investigation explicitly demonstrates the vulnerability of 2D toric codes to quantum deviations in code space. △ Less

Submitted 8 March, 2025; v1 submitted 30 January, 2023; originally announced January 2023.

Comments: Published online: 12 pages, 5 figures, 1 table, with 21 pages supplemental Information]

Journal ref: PNAS Nexus, pgaf063 (2025)

Information scrambling and entanglement in quantum approximate optimization algorithm circuits

Authors: Chen Qian, Wei-Feng Zhuang, Rui-Cheng Guo, Meng-Jun Hu, Dong E. Liu

Abstract: Variational quantum algorithms, which consist of optimal parameterized quantum circuits, are promising for demonstrating quantum advantages in the noisy intermediate-scale quantum (NISQ) era. Apart from classical computational resources, different kinds of quantum resources have their contributions to the process of computing, such as information scrambling and entanglement. Characterizing the rel… ▽ More Variational quantum algorithms, which consist of optimal parameterized quantum circuits, are promising for demonstrating quantum advantages in the noisy intermediate-scale quantum (NISQ) era. Apart from classical computational resources, different kinds of quantum resources have their contributions to the process of computing, such as information scrambling and entanglement. Characterizing the relation between the complexity of specific problems and quantum resources consumed by solving these problems is helpful for us to understand the structure of VQAs in the context of quantum information processing. In this work, we focus on the quantum approximate optimization algorithm (QAOA), which aims to solve combinatorial optimization problems. We study information scrambling and entanglement in QAOA circuits, respectively, and discover that for a harder problem, more quantum resource is required for the QAOA circuit to obtain the solution in most cases. We note that in the future, our results can be used to benchmark the complexity of quantum many-body problems by information scrambling or entanglement accumulation in the computing process. △ Less

Submitted 26 December, 2024; v1 submitted 18 January, 2023; originally announced January 2023.

Comments: 11 pages, 12 figures

Journal ref: Eur. Phys. J. Plus 139, 14 (2024)

Benchmarking universal quantum gates via channel spectrum

Authors: Yanwu Gu, Wei-Feng Zhuang, Xudan Chai, Dong E. Liu

Abstract: Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limita… ▽ More Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of global entangling gates and frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation. △ Less

Submitted 21 September, 2023; v1 submitted 5 January, 2023; originally announced January 2023.

Comments: 14 pages, 5 figures, Published version

Journal ref: Nature Communications, 14, 5880 (2023)

Noise-resilient phase estimation with randomized compiling

Authors: Yanwu Gu, Yunheng Ma, Nicolo Forcellini, Dong E. Liu

Abstract: We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the noise channels with only Hermitian Kraus operators do not change the phases of a unitary operator, and therefore, the benign types of noise for phase estimation are identified. By using the randomized compiling protocol, we can convert the generic noise in the… ▽ More We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the noise channels with only Hermitian Kraus operators do not change the phases of a unitary operator, and therefore, the benign types of noise for phase estimation are identified. By using the randomized compiling protocol, we can convert the generic noise in the phase estimation circuits into stochastic Pauli noise, which satisfies the condition of our theorem. Thus we achieve a noise-resilient phase estimation without any quantum resource overhead. The simulated experiments show that our method can significantly reduce the estimation error of the phases by up to two orders of magnitude. Our method paves the way for the utilization of quantum phase estimation before the advent of fault-tolerant quantum computers. △ Less

Submitted 22 June, 2023; v1 submitted 8 August, 2022; originally announced August 2022.

Comments: 5 pages 4 figures, with the appendix; final version for publication

Journal ref: Phys. Rev. Lett. 130, 250601 (2023)

Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Continuous Measurements

Authors: Qinghong Yang, Yi Zuo, Dong E. Liu

Abstract: Quantum entanglement phase transitions have provided new insights to quantum many-body dynamics. Both disorders and measurements are found to induce similar entanglement transitions. Here, we provide a theoretical framework that unifies these two seemingly disparate concepts and discloses their internal connections. Specifically, we analytically analyze a $d$-dimension free-fermion gas subject to… ▽ More Quantum entanglement phase transitions have provided new insights to quantum many-body dynamics. Both disorders and measurements are found to induce similar entanglement transitions. Here, we provide a theoretical framework that unifies these two seemingly disparate concepts and discloses their internal connections. Specifically, we analytically analyze a $d$-dimension free-fermion gas subject to continuous projective measurements. By mapping the Lindblad master equation to the functional Keldysh field theory, we develop an effective theory termed as the time-local Keldysh nonlinear sigma model, which enables us to analytically describe the physics of the monitored system. Our effective theory resembles to that used to describe the disordered fermionic systems. As an application of the effective theory, we study the transport property and obtain a Drude-form conductivity where the elastic scattering time is replaced by the inverse measurement strength. According to these similarities, two different concepts, measurements and disorders, are unified in the same theoretical framework. A numerical verification of our theory and predictions is also provided. △ Less

Submitted 13 September, 2023; v1 submitted 7 July, 2022; originally announced July 2022.

Comments: Revised version with the updated main text, reference list, supplementary information including a new numerical caluclation

Journal ref: Phys. Rev. Research 5, 033174 (2023)

Fast Quantum Calibration using Bayesian Optimization with State Parameter Estimator for Non-Markovian Environment

Authors: Peng Qian, Shahid Qamar, Xiao Xiao, Yanwu Gu, Xudan Chai, Zhen Zhao, Nicolo Forcellini, Dong E. Liu

Abstract: As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very sensitive to the external environment, with control hardware parameters slowly drifting during operation, affecting gate fidelity. Currently, existing calibration… ▽ More As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very sensitive to the external environment, with control hardware parameters slowly drifting during operation, affecting gate fidelity. Currently, existing calibration techniques require complex and lengthy measurements to independently control the different parameters of each gate and are unscalable to large quantum systems. Therefore, fully automated protocols with the desired functionalities are required to speed up the calibration process. This paper aims to propose single-qubit calibration of superconducting qubits under continuous weak measurements from a real physical experimental settings point of view. We propose a real-time optimal estimator of qubit states, which utilizes weak measurements and Bayesian optimization to find the optimal control pulses for gate design. Our numerical results demonstrate a significant reduction in the calibration process, obtaining a high gate fidelity. Using the proposed estimator we estimated the qubit state with and without measurement noise and the estimation error between the qubit state and the estimator state is less than 0.02. With this setup, we drive an approximated pi pulse with final fidelity of 0.9928. This shows that our proposed strategy is robust against the presence of measurement and environmental noise and can also be applicable for the calibration of many other quantum computation technologies. △ Less

Submitted 25 May, 2022; originally announced May 2022.

Comments: 15 pages, 8 figures, 1 table

Quantum circuit architecture search on a superconducting processor

Authors: Kehuan Linghu, Yang Qian, Ruixia Wang, Meng-Jun Hu, Zhiyuan Li, Xuegang Li, Huikai Xu, Jingning Zhang, Teng Ma, Peng Zhao, Dong E. Liu, Min-Hsiu Hsieh, Xingyao Wu, Yuxuan Du, Dacheng Tao, Yirong Jin, Haifeng Yu

Abstract: Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale q… ▽ More Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale quantum (NISQ) machines. To address this issue, here we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz towards classification tasks. Compared with the heuristic ansatze, the ansatz designed by QAS improves test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansatze. Our work provides concrete guidance for developing variable ansatze to tackle various large-scale quantum learning problems with advantages. △ Less

Submitted 3 January, 2022; originally announced January 2022.

Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits

Authors: Wei-Feng Zhuang, Ya-Nan Pu, Hong-Ze Xu, Xudan Chai, Yanwu Gu, Yunheng Ma, Shahid Qamar, Chen Qian, Peng Qian, Xiao Xiao, Meng-Jun Hu, Dong E. Liu

Abstract: The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since the core of QAOA is the computation… ▽ More The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since the core of QAOA is the computation of expectation values of the problem Hamiltonian, an important practical question is whether we can find an efficient classical algorithm to solve quantum mean value in the case of general shallow quantum circuits. Here, we present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits in most optimization problems except for complete graph case. Numerical tests in Max-cut, graph coloring and Sherrington-Kirkpatrick model problems, compared to the state-of-the-art method, shows orders of magnitude performance improvement. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors. △ Less

Submitted 21 December, 2021; originally announced December 2021.

An analytic study of the independent coherent errors in the surface code

Authors: Yuanchen Zhao, Dong E. Liu

Abstract: The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more detrimental and hard to analyze compared to those ideal stochastic errors. In this paper, we study the independent coherent error due to the imperfect unitary… ▽ More The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more detrimental and hard to analyze compared to those ideal stochastic errors. In this paper, we study the independent coherent error due to the imperfect unitary rotation on each physical qubit of the toric code. We find that the surface code under coherent error satisfies generalized Knill-Laflamme (K-L) criterion and falls into the category of approximate QEC. The extra term in the generalized K-L criterion corresponds to the coherent part of the error channel at logical level, and then show that the generalized K-L criterion approaches the normal K-L criterion when the code distance becomes large. In addition, we also find that if the code with a fixed distance d is $ε$-correctable, the value of $ε$ describing the accuracy of the approximate QEC cannot be smaller than a lower bound. We then study the success probability of QEC under such coherent errors, and confirm that the exact success probability under coherent error is smaller than the results using Pauli twirling approximation at physical level. △ Less

Submitted 1 December, 2021; originally announced December 2021.

Comments: 15 pages, 6 figures

Effect of quantum error correction on detection-induced coherent errors

Authors: Qinghong Yang, Dong E. Liu

Abstract: We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promising surface code, we find that the detection-induced coherent error will result in undetected error terms, which will accumulate and evolve into log… ▽ More We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promising surface code, we find that the detection-induced coherent error will result in undetected error terms, which will accumulate and evolve into logical errors. However, we show that such errors will be alleviated by increasing the code size, akin to eliminating other types of errors discussed previously. We also find that with detection-induced coherent errors, the exact surface code becomes an approximate QECC. △ Less

Submitted 24 February, 2022; v1 submitted 19 July, 2021; originally announced July 2021.

Comments: 9 pages, 3 figures

Journal ref: Phys. Rev. A 105, 022434 (2022)

Readout of Majorana bound states via Landau-Zener transition

Authors: Zhen-Tao Zhang, Dong E. Liu

Abstract: Reading out Majorana bound states (MBSs) is essential both to verify their non-Abelian property and to realize topological quantum computation. Here, we construct a protocol to measure the parity of two MBSs in a Majorana island coupled to double quantum dot (DQD). The parity information is mapped to the charge state of the DQD through Landau-Zener transition. The operation needed is sweeping the… ▽ More Reading out Majorana bound states (MBSs) is essential both to verify their non-Abelian property and to realize topological quantum computation. Here, we construct a protocol to measure the parity of two MBSs in a Majorana island coupled to double quantum dot (DQD). The parity information is mapped to the charge state of the DQD through Landau-Zener transition. The operation needed is sweeping the bias of the DQD, which is followed by charge sensing. In the case without fine-tuning, a single run of sweep-and-detection implement a weak measurement of the parity. We find that in general a sequence of about ten runs would completely project a superposition state to either parity, and the charge detection in each run records how the state of MBSs collapses step by step. Remarkably, this readout protocol is of non-demolition and robust to low frequency charge fluctuation. △ Less

Submitted 12 September, 2021; v1 submitted 10 December, 2020; originally announced December 2020.

Comments: 7 pages, 5 figures

Journal ref: Phys. Rev. B 103, 195401 (2021)

A hierarchy in Majorana non-abelian tests and hidden variable models

Authors: Peng Qian, Dong E. Liu

Abstract: The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary in order to develop loophole-free tests. We introduce a series of classical… ▽ More The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary in order to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity. △ Less

Submitted 26 July, 2020; originally announced July 2020.

Comments: 5 pages, 4 figures, 5 page supplementary

Journal ref: Chin. Phys. Lett. 40, 100501 (2023)

How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon

Authors: Christina Knapp, Michael Zaletel, Dong E. Liu, Meng Cheng, Parsa Bonderson, Chetan Nayak

Abstract: Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In… ▽ More Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry's matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error. △ Less

Submitted 23 August, 2016; v1 submitted 21 January, 2016; originally announced January 2016.

Comments: 33 pages, 18 figures, version 3: extended results to general anyon braiding

Journal ref: Phys. Rev. X 6, 041003 (2016)

Thermalization mechanism for time-periodic finite isolated interacting quantum systems

Authors: Dong E. Liu

Abstract: We present a theory to describe thermalization mechanism for time-periodic finite isolated interacting quantum systems. The long time asymptote of natural observables in Floquet states is directly related to averages of these observables governed by a time-independent effective Hamiltonian. We prove that if the effective system is nonintegrable and satisfies eigenstate thermalization hypothesis, q… ▽ More We present a theory to describe thermalization mechanism for time-periodic finite isolated interacting quantum systems. The long time asymptote of natural observables in Floquet states is directly related to averages of these observables governed by a time-independent effective Hamiltonian. We prove that if the effective system is nonintegrable and satisfies eigenstate thermalization hypothesis, quantum states of such time-periodic isolated systems will thermalize. After a long time evolution, system will relax to a stationary state, which only depends on an initial energy of the effective Hamiltonian and follows a generalized eigenstate thermalization hypothesis. A numerical test for the periodically modulated Bose-Hubbard model, with the extra nearest neighbor interaction on the bosonic lattice, agrees with the theoretical predictions. △ Less

Submitted 11 October, 2014; originally announced October 2014.

Comments: 6 pages, 4 figures

Classification of Floquet Statistical Distribution for Time-Periodic Open Systems

Authors: Dong E. Liu

Abstract: How to understand the order of Floquet stationary states in the presence of external bath coupling and their statistical mechanics is challenging; the answers are important for preparations and control of those Floquet states. Here, we propose a scheme to classify the statistical distribution of Floquet states for time-periodic systems which couple to an external heat bath. If an effective Hamilto… ▽ More How to understand the order of Floquet stationary states in the presence of external bath coupling and their statistical mechanics is challenging; the answers are important for preparations and control of those Floquet states. Here, we propose a scheme to classify the statistical distribution of Floquet states for time-periodic systems which couple to an external heat bath. If an effective Hamiltonian and a system-bath coupling operator, which are all time-independent, can be simultaneously obtained via a time-periodic unitary transformation, the statistical mechanics of the Floquet states is equivalent to the equilibrium statistical mechanics of the effective Hamiltonian. In the large driving frequency cases, we also show that the conditions of this theorem can be weakened to: the time-period part in the system Hamiltonian commutes with the system-bath coupling operator. A Floquet-Markov approach is applied to numerically compute the Floquet state occupation distribution of a bosonic chain, and the results agree with the theoretical predictions. △ Less

Submitted 7 April, 2015; v1 submitted 3 October, 2014; originally announced October 2014.

Comments: 5 pages, 2 figures. reference updated

Journal ref: Phys. Rev. B 91, 144301 (2015)

Floquet Majorana Fermions for Topological Qubits

Authors: Dong E. Liu, Alex Levchenko, Harold U. Baranger

Abstract: We introduce and develop an approach to realizing a topological phase transition and non-Abelian statistics with dynamically induced Floquet Majorana Fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasi-energy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter spac… ▽ More We introduce and develop an approach to realizing a topological phase transition and non-Abelian statistics with dynamically induced Floquet Majorana Fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasi-energy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space with large quasi-energy gaps, which prevents transitions to other Floquet states under adiabatic driving. We also show that in the asymptotic limit FMFs preserve non-Abelian statistics and, thus, behave like their equilibrium counterparts. △ Less

Submitted 8 November, 2012; v1 submitted 6 November, 2012; originally announced November 2012.

Comments: 4 pages, 2 figures; supplementary information: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 111, 047002 (2013)