Showing 1–50 of 91 results for author: Liu, D E

Tip-Tuned Renormalization-Group Spectroscopy Unmasks a False-positive Topological Superconducting Vortex

Authors: Zhenhua Zhu, Qun Zhu, Yong-Wei Wang, Gu Zhang, Jihai Zhang, Xu-Cun Ma, Qi-Kun Xue, Can-Li Song, Dong E. Liu

Abstract: Clean, nonsplit vortex zero-bias peaks (ZBPs) can be misinterpreted as Majorana zero modes (MZMs), making static scanning tunneling microscopy intrinsically ambiguous. Here we use the STM tip coupling to drive a local boundary-renormalization-group (boundary RG) flow, turning dynamical Coulomb blockade into a falsification test for Majorana-like ZBPs. Experimentally, in a $\mathrm{SrSn}_3$ thin fi… ▽ More Clean, nonsplit vortex zero-bias peaks (ZBPs) can be misinterpreted as Majorana zero modes (MZMs), making static scanning tunneling microscopy intrinsically ambiguous. Here we use the STM tip coupling to drive a local boundary-renormalization-group (boundary RG) flow, turning dynamical Coulomb blockade into a falsification test for Majorana-like ZBPs. Experimentally, in a $\mathrm{SrSn}_3$ thin film, normal-state spectra establish an Ohmic dissipative environment, and a common boundary-RG/thermodynamic-Bethe-ansatz analysis of the superconducting-gap and vortex-center spectra yields consistent dissipation strengths within the $r < 1/2$ Majorana-filter regime. Lowering the tip nevertheless drives a clean, non-split vortex-center ZBP into a zero-bias dip, opposite to the protected flow of an isolated MZM, unmasking the peak as a Majorana false positive produced by a conventional vortex-core state. The same flow selectively suppresses the strongly tip-coupled channel, resolving the two-gap superconductivity. Dissipative STM thus tests dynamical protection rather than spectral appearance. △ Less

Submitted 28 July, 2026; originally announced July 2026.

Comments: 13 pages, 6 figures

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

Charge Density Wave Driven Topological Phase Transition in Vortices

Authors: Zhenhua Zhu, Ziqiang Wang, Dong E. Liu

Abstract: The interplay between charge density waves (CDWs) and superconductivity is a central theme in quantum materials, yet how CDW phase textures govern vortex topology remains poorly understood. We develop a theoretical framework showing that the phase of a stripe CDW can switch a magnetic vortex between topological and trivial regimes. Motivated by recent experiments, we propose two candidate mechanis… ▽ More The interplay between charge density waves (CDWs) and superconductivity is a central theme in quantum materials, yet how CDW phase textures govern vortex topology remains poorly understood. We develop a theoretical framework showing that the phase of a stripe CDW can switch a magnetic vortex between topological and trivial regimes. Motivated by recent experiments, we propose two candidate mechanisms enabling phase-controlled switching of vortex topology. In a direct-modulation scenario, the CDW acts as a periodic potential that locally renormalizes band parameters and can induce topological transitions, but it generally cannot reproduce the symmetric node/antinode trend without fine tuning. In contrast, in an inversion-symmetry-breaking (ISB) scenario, a CDW node pinned to the vortex center breaks local inversion and allows for the mixture of spin-triplet pairing of Cooper pairs, producing a robust topological transition when this component dominates. Our results suggests CDW phase as a possible local handle to tune and test vortex topology. △ Less

Submitted 17 April, 2026; originally announced April 2026.

Comments: 9 pages, 5 figures

Intertwined Charge Stripes and Majorana Zero Modes in An Iron-Based Superconductor

Authors: Yu Liu, Li-Xuan Wei, Qiang-Jun Cheng, Zhenhua Zhu, Xin-Yu Shi, Cong-Cong Lou, Yong-Wei Wang, Ze-Xian Deng, Ming-Qiang Ren, Dong E. Liu, Ziqiang Wang, Xu-Cun Ma, Jin-Feng Jia, Qi-Kun Xue, Can-Li Song

Abstract: In type-II superconductors, magnetic fields modulate the amplitude and phase of the superconducting order parameter, forming quantized vortices where superconductivity is locally suppressed and exotic bound states or competing electronic orders emerge. Using spectroscopic-imaging scanning tunneling microscopy on epitaxial Ba(Fe$_{0.94}Co$_{0.06})$_2$As$_2$ films, we discover an incommensurate char… ▽ More In type-II superconductors, magnetic fields modulate the amplitude and phase of the superconducting order parameter, forming quantized vortices where superconductivity is locally suppressed and exotic bound states or competing electronic orders emerge. Using spectroscopic-imaging scanning tunneling microscopy on epitaxial Ba(Fe$_{0.94}Co$_{0.06})$_2$As$_2$ films, we discover an incommensurate charge-stripe order aligned with the Fe-Fe bond direction and nucleated inside magnetic vortices. These charge modulations intensify at the vortex core, extend far into the vortex halo, and persist within the superconducting gap. Strikingly, the charge order modulates Andreev bound states of vortices at non-zero energies, producing abelian vortices with half-odd-integer level quantization and non-abelian vortices with integer-quantized core states that host a Majorana zero mode. The distinct vortex types are distinguished by the registry of their centers relative to the charge-stripe pattern and remain robust in ultrathin (2.5-unit-cell) films. Our findings reveal a density-wave-textured vortex matter and provide fresh insights into the intertwined phenomena of charge-stripe order, pair-density-wave modulations, and Majorana physics in iron-based superconductors. △ Less

Submitted 22 January, 2026; originally announced January 2026.

Comments: 17 pages, 4 figures, Supplemental Material

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)

Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system

Authors: Fei Yang, Dong E. Liu

Abstract: Conventional wisdom holds that static disorder is indispensable to the integer quantum Hall effect, underpinning both quantized plateaus and the plateau-plateau transition. We show that pure dephasing, without elastic disorder, is sufficient to generate the same $θ$ driven criticality. Starting from a Keldysh formulation, we derive an open system nonlinear $σ$ model (NL$σ$M) for class A with a top… ▽ More Conventional wisdom holds that static disorder is indispensable to the integer quantum Hall effect, underpinning both quantized plateaus and the plateau-plateau transition. We show that pure dephasing, without elastic disorder, is sufficient to generate the same $θ$ driven criticality. Starting from a Keldysh formulation, we derive an open system nonlinear $σ$ model (NL$σ$M) for class A with a topological $θ$ term but no Cooperon sector, and we demonstrate that nonperturbative instantons still govern a two parameter flow of $(σ_{xx},σ_{xy})$. Evaluating $θ$ in a dephasing quantum anomalous Hall setting, we predict a quantum Hall critical point at $σ_{xy}=1/2$ with finite $σ_{xx}$ the hallmark of the integer quantum Hall universality class realized without Anderson localization. Boundary driven simulations of the Qi_Wu_Zhang model with local dephasing confirm this prediction and provide an experimentally aligned protocol to extract $(σ_{xx},σ_{xy})$ from Hall potential maps. By establishing dephasing as a self contained route to Hall criticality, our framework reframes plateau physics in open solid state and cold atom platforms and offers practical diagnostics for topological transport in nonunitary matter. △ Less

Submitted 9 November, 2025; originally announced November 2025.

Comments: 13 pages, 6 figures

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)

Coulomb blockade in open superconducting islands on InAs nanowires

Authors: Huading Song, Zhaoyu Wang, Dong Pan, Jiaye Xu, Yuqing Wang, Zhan Cao, Dong E. Liu, Ke He, Runan Shang, Jianhua Zhao, Hao Zhang

Abstract: Electrons in closed systems can exhibit Coulomb blockade (CB) oscillations due to charge quantization. Here, we report CB oscillations in aluminum superconducting islands on InAs nanowires in the open regime. The Al island is connected to the source/drain leads through two contacts: One is fully transmitting while the other is tuned into the tunneling regime. This device configuration is typical f… ▽ More Electrons in closed systems can exhibit Coulomb blockade (CB) oscillations due to charge quantization. Here, we report CB oscillations in aluminum superconducting islands on InAs nanowires in the open regime. The Al island is connected to the source/drain leads through two contacts: One is fully transmitting while the other is tuned into the tunneling regime. This device configuration is typical for tunneling spectroscopy where charging energy is generally considered negligible. The oscillation periods are 2$e$ or 1$e$, depending on the gate settings. A magnetic field can induce the 2$e$ to 1$e$ transition. Our result is reminiscent of the "mesoscopic Coulomb blockade" in open quantum dots caused by electron interference. △ Less

Submitted 9 October, 2024; originally announced October 2024.

Journal ref: Phys. Rev. B 111 (2025) L201402

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.

Quantized Andreev conductance in semiconductor nanowires

Authors: Yichun Gao, Wenyu Song, Yuhao Wang, Zuhan Geng, Zhan Cao, Zehao Yu, Shuai Yang, Jiaye Xu, Fangting Chen, Zonglin Li, Ruidong Li, Lining Yang, Zhaoyu Wang, Shan Zhang, Xiao Feng, Tiantian Wang, Yunyi Zang, Lin Li, Dong E. Liu, Runan Shang, Qi-Kun Xue, Ke He, Hao Zhang

Abstract: Clean one-dimensional electron systems can exhibit quantized conductance. The plateau conductance doubles if the transport is dominated by Andreev reflection. Here, we report quantized conductance observed in both Andreev and normal-state transports in PbTe-Pb and PbTe-In hybrid nanowires. The Andreev plateau is observed at $4e^2/h$, twice of the normal plateau value of $2e^2/h$. In comparison, An… ▽ More Clean one-dimensional electron systems can exhibit quantized conductance. The plateau conductance doubles if the transport is dominated by Andreev reflection. Here, we report quantized conductance observed in both Andreev and normal-state transports in PbTe-Pb and PbTe-In hybrid nanowires. The Andreev plateau is observed at $4e^2/h$, twice of the normal plateau value of $2e^2/h$. In comparison, Andreev conductance in the best-optimized III-V nanowires is non-quantized due to mode-mixing induced dips (a disorder effect), despite the quantization of normal-state transport. The negligible mode mixing in PbTe hybrids indicates an unprecedented low-disorder transport regime for nanowire devices, beneficial for Majorana researches. △ Less

Submitted 17 June, 2024; originally announced June 2024.

Journal ref: Phys. Rev. Applied 23, L061004 (2025)

Gate-tunable subband degeneracy in semiconductor nanowires

Authors: Yuhao Wang, Wenyu Song, Zhan Cao, Zehao Yu, Shuai Yang, Zonglin Li, Yichun Gao, Ruidong Li, Fangting Chen, Zuhan Geng, Lining Yang, Jiaye Xu, Zhaoyu Wang, Shan Zhang, Xiao Feng, Tiantian Wang, Yunyi Zang, Lin Li, Runan Shang, Qi-Kun Xue, Dong E. Liu, Ke He, Hao Zhang

Abstract: Degeneracy and symmetry have a profound relation in quantum systems. Here, we report gate-tunable subband degeneracy in PbTe nanowires with a nearly symmetric cross-sectional shape. The degeneracy is revealed in electron transport by the absence of a quantized plateau. Utilizing a dual gate design, we can apply an electric field to lift the degeneracy, reflected as emergence of the plateau. This d… ▽ More Degeneracy and symmetry have a profound relation in quantum systems. Here, we report gate-tunable subband degeneracy in PbTe nanowires with a nearly symmetric cross-sectional shape. The degeneracy is revealed in electron transport by the absence of a quantized plateau. Utilizing a dual gate design, we can apply an electric field to lift the degeneracy, reflected as emergence of the plateau. This degeneracy and its tunable lifting were challenging to observe in previous nanowire experiments, possibly due to disorder. Numerical simulations can qualitatively capture our observation, shedding light on device parameters for future applications. △ Less

Submitted 3 April, 2024; originally announced April 2024.

Journal ref: PNAS 121, e2406884121 (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)

Anomalous Fraunhofer-like patterns in quantum anomalous Hall Josephson junction

Authors: Junjie Qi, Haiwen Liu, Jie Liu, Hua Jiang, Dong E. Liu, Chui-Zhen Chen, Ke He, X. C. Xie

Abstract: The intriguing interplay between topology and superconductivity has attracted significant attention, given its potential for realizing topological superconductivity. In the quantum anomalous Hall insulators (QAHIs)-based junction, the supercurrents are carried by the chiral edge states, characterized by a $2Φ_0$ magnetic flux periodicity ($Φ_0 = h/2e$ is the flux quantum, $h$ the Planck constant,… ▽ More The intriguing interplay between topology and superconductivity has attracted significant attention, given its potential for realizing topological superconductivity. In the quantum anomalous Hall insulators (QAHIs)-based junction, the supercurrents are carried by the chiral edge states, characterized by a $2Φ_0$ magnetic flux periodicity ($Φ_0 = h/2e$ is the flux quantum, $h$ the Planck constant, and $e$ the electron charge). However, experimental observations indicate the presence of bulk carriers in QAHI samples due to magnetic dopants. In this study, we reveal a systematic transition from edge-state to bulk-state dominant supercurrents as the chemical potential varies from the bulk gap to the conduction band. This results in an evolution from a $2Φ_0$-periodic oscillation pattern to an asymmetric Fraunhofer pattern. Furthermore, a novel Fraunhoher-like pattern emerges due to the coexistence of chiral edge states and bulk states caused by magnetic {\color{black}domains}, even when the chemical potential resides within the gap. These findings not only advance the theoretical understanding but also pave the way for the experimental discovery of the chiral Josephson effect based on QAHI doped with magnetic impurities. △ Less

Submitted 11 November, 2024; v1 submitted 30 November, 2023; originally announced December 2023.

Comments: 8 pages, 8 figures

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.

Electrostatic environment and Majorana bound states in full-shell topological insulator nanowires

Authors: Li Chen, Xiao-Hong Pan, Zhan Cao, Dong E. Liu, Xin Liu

Abstract: The combination of a superconductor (SC) and a topological insulator (TI) nanowire was proposed as a potential candidate for realizing Majorana zero modes (MZMs). In this study, we adopt the Schrödinger-Poisson formalism to incorporate the electrostatic environment inside the nanowire and systematically explore its topological properties. Our calculations reveal that the proximity to the SC induce… ▽ More The combination of a superconductor (SC) and a topological insulator (TI) nanowire was proposed as a potential candidate for realizing Majorana zero modes (MZMs). In this study, we adopt the Schrödinger-Poisson formalism to incorporate the electrostatic environment inside the nanowire and systematically explore its topological properties. Our calculations reveal that the proximity to the SC induces a band bending effect, leading to a non-uniform potential across the TI nanowire. As a consequence, there is an upward shift of the Fermi level within the conduction band. This gives rise to the coexistence of surface and bulk states, localized in an accumulation layer adjacent to the TI-SC interface. When magnetic flux is applied, these occupied states have different flux-penetration areas, suppressing the superconducting gap. However, this impact can be mitigated by increasing the radius of the nanowire. Finally, We demonstrate that MZMs can be achieved across a wide range of parameters centered around one applied flux quantum, $φ_0 = h/2e$. Within this regime, MZMs can be realized even in the presence of conduction bands, which are not affected by the band bending effect. These findings provide valuable insights into the practical realization of MZMs in TI nanowire-based devices, especially in the presence of a complicated electrostatic environment. △ Less

Submitted 22 September, 2023; v1 submitted 20 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)

Enhanced localization in the prethermal regime of continuously measured many-body localized systems

Authors: Kristian Patrick, Qinghong Yang, Dong E. Liu

Abstract: Many-body localized systems exhibit a unique characteristic of avoiding thermalization, primarily attributed to the presence of a local disorder potential in the Hamiltonian. In recent years there has been an interest in simulating these systems on quantum devices. However, actual quantum devices are subject to unavoidable decoherence that can be modeled as coupling to a bath or continuous measure… ▽ More Many-body localized systems exhibit a unique characteristic of avoiding thermalization, primarily attributed to the presence of a local disorder potential in the Hamiltonian. In recent years there has been an interest in simulating these systems on quantum devices. However, actual quantum devices are subject to unavoidable decoherence that can be modeled as coupling to a bath or continuous measurements. The quantum Zeno effect is also known to inhibit thermalization in a quantum system, where repeated measurements suppress transport. In this work we study the interplay of many-body localization and the many-body quantum Zeno effect. In a prethermal regime, we find that signatures of many-body localization are enhanced when the system is coupled to a bath that contains measurements of local fermion population, subject to the appropriate choice of system and bath parameters. △ Less

Submitted 27 November, 2024; v1 submitted 22 July, 2023; originally announced July 2023.

Comments: Published version. 10 pages, 5 figures, including Supplementary Materials

Journal ref: Physical Review B 110, 184211 (2024)

Conductance Quantization in PbTe Nanowires

Authors: Wenyu Song, Yuhao Wang, Wentao Miao, Zehao Yu, Yichun Gao, Ruidong Li, Shuai Yang, Fangting Chen, Zuhan Geng, Zitong Zhang, Shan Zhang, Yunyi Zang, Zhan Cao, Dong E. Liu, Runan Shang, Xiao Feng, Lin Li, Qi-Kun Xue, Ke He, Hao Zhang

Abstract: PbTe nanowires coupled to a superconductor have recently been proposed as a potential Majorana platform. The hallmark of the one-dimensional nature of ballistic nanowires is their quantized conductance. Here, we report the observation of conductance plateaus at multiples of the quantized value $2e^2/h$ in PbTe nanowires at finite magnetic fields. The quantized plateaus, as a function of source-dra… ▽ More PbTe nanowires coupled to a superconductor have recently been proposed as a potential Majorana platform. The hallmark of the one-dimensional nature of ballistic nanowires is their quantized conductance. Here, we report the observation of conductance plateaus at multiples of the quantized value $2e^2/h$ in PbTe nanowires at finite magnetic fields. The quantized plateaus, as a function of source-drain bias and magnetic field, allow for the extraction of the Landé $g$-factor, sub-band spacing and effective mass. The coefficient of 2 in the plateau conductance indicates the presence of valley degeneracy arising from the crystal orientation of the nanowires, which are grown on a (001) substrate. Occasionally, this degeneracy can be lifted by a gate voltage that breaks the mirror symmetry. Our results demonstrate the one-dimensionality of PbTe nanowires and fulfill one of the necessary conditions for the realization of Majorana zero modes. △ Less

Submitted 20 April, 2023; originally announced April 2023.

Comments: Raw data and processing codes within this paper are available at: https://doi.org/10.5281/zenodo.7848599

Journal ref: Phys. Rev. B 108, 045426 (2023)

Influence of topological degeneracy on the boundary Berezinskii-Kosterlitz-Thouless quantum phase transition of a dissipative resonant level

Authors: Gu Zhang, Zhan Cao, Dong E. Liu

Abstract: The interplay between a topological degeneracy and the residue degeneracy (also known as the residue entropy) of quantum criticality remains as an important but not thoroughly understood topic. We find that this topological degeneracy, provided by a Majorana zero mode pair, relaxes the otherwise strictly requested symmetry requirement, to observe the boundary Berezinskii-Kosterlitz-Thouless (BKT)… ▽ More The interplay between a topological degeneracy and the residue degeneracy (also known as the residue entropy) of quantum criticality remains as an important but not thoroughly understood topic. We find that this topological degeneracy, provided by a Majorana zero mode pair, relaxes the otherwise strictly requested symmetry requirement, to observe the boundary Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition (QPT) of a dissipative resonant level. Our work indicates that the topological degeneracy can be potentially viewed as an auxiliary symmetry that realizes a robust boundary QPT. The relaxation of the symmetry requirement extends the transition from a point to a finite area, thus greatly reducing the difficulty to experimentally observe the QPT. This topology-involved exotic BKT phase diagram, on the other hand, provides another piece of evidence that can further confirm the existence of a Majorana zero mode. △ Less

Submitted 26 April, 2024; v1 submitted 20 March, 2023; originally announced March 2023.

Comments: 14 pages and 8 figures

Journal ref: Phys. Rev. B.109, L161110 (2024)

Meissner effect induced Majorana zero modes at small magnetic field

Authors: Xiao-Hong Pan, Li Chen, Dong E. Liu, Fu-Chun Zhang, Xin Liu

Abstract: One fundamental difficulty in realizing Majorana zero modes (MZMs) is the required high magnetic field, which causes serious issues, e.g., shrinks the superconducting gap, reduces topological region, and weakens their robustness against disorder. In this work, we propose that the Meissner effect can bring the topological superconducting phase to a superconductor/topological-insulator/superconducto… ▽ More One fundamental difficulty in realizing Majorana zero modes (MZMs) is the required high magnetic field, which causes serious issues, e.g., shrinks the superconducting gap, reduces topological region, and weakens their robustness against disorder. In this work, we propose that the Meissner effect can bring the topological superconducting phase to a superconductor/topological-insulator/superconductor (SC/TI/SC) hybrid system. Remarkably, the required magnetic field strength ($<$10 mT) to support MZMs has been reduced by several orders of magnitude compared to that ($>$0.5 T) in the previous schemes. Tuning the phase difference between the top and bottom superconductors can control the number and position of the MZMs. In addition, we account for the electrostatic potential in the superconductor/topological-insulator (SC/TI) interface through the self-consistent Schrödinger-Poisson calculation, which shows the experimental accessibility of our proposal. Our proposal only needs a small magnetic eld of less than 10 mT and is robust against the chemical potential fluctuation, which makes SC/TI/SC hybrid an ideal Majorana platform. △ Less

Submitted 9 February, 2023; originally announced February 2023.

Comments: 7 pages, 4 figures, and Supplemental material

Journal ref: Physical Review Letters 132, 036602 (2024)

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)

Properties of dissipative Floquet Majorana modes using a quantum dot

Authors: Nicolò Forcellini, Zhan Cao, Dong E. Liu

Abstract: We study the electronic conductance of dissipative Floquet Majorana zero modes (FMZMs) in a periodically driven nanowire coupled to a quantum dot. We use a numerical method which can accurately take into account the dissipation effects from the superconducting bath, which causes the FMZMs to have a finite lifetime. Our results show that, in the weak nanowire-dot coupling regime, the peak conductan… ▽ More We study the electronic conductance of dissipative Floquet Majorana zero modes (FMZMs) in a periodically driven nanowire coupled to a quantum dot. We use a numerical method which can accurately take into account the dissipation effects from the superconducting bath, which causes the FMZMs to have a finite lifetime. Our results show that, in the weak nanowire-dot coupling regime, the peak conductance at zero temperature of the resonant dot can be well approximated by a universal function of the FMZM lifetime rescaled with the nanowire-dot coupling strength: For a long FMZM's lifetime, the conductance approaches the characteristic quantized value of $G = e^2/2h$, whereas $G \rightarrow e^2/h$ (uncoupled dot) as the FMZMs' lifetime goes to zero. In principle, our method can be used to test the presence and lifetime of FMZMs in such devices, which is key for any practical application of these topological states. △ Less

Submitted 20 January, 2023; originally announced January 2023.

Comments: 11 pages, 5 figures

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)

Differential current noise as an identifier of Andreev bound states that induce nearly quantized conductance plateaus

Authors: Zhan Cao, Gu Zhang, Hao Zhang, Ying-Xin Liang, Wan-Xiu He, Ke He, Dong E. Liu

Abstract: Quantized conductance plateaus, a celebrated hallmark of Majorana bound states (MBSs) predicted a decade ago, have recently been observed with small deviations in iron-based superconductors and hybrid nanowires. Here, we demonstrate that nearly quantized conductance plateaus can also arise from trivial Andreev bound states (ABSs). To avoid ABS interruptions, we propose identifying ABS-induced quan… ▽ More Quantized conductance plateaus, a celebrated hallmark of Majorana bound states (MBSs) predicted a decade ago, have recently been observed with small deviations in iron-based superconductors and hybrid nanowires. Here, we demonstrate that nearly quantized conductance plateaus can also arise from trivial Andreev bound states (ABSs). To avoid ABS interruptions, we propose identifying ABS-induced quantized conductance plateaus by measuring the associated differential current noise $P$ versus bias voltage $V$. Specifically, for a quantized conductance plateau induced by one or multiple low-energy ABSs, the associated $P(V)$ curve exhibits a double-peak around zero bias, with the peak positions at $e|V|\approx 3k_B T$ (where $T$ is the temperature) and peak values larger than $2e^3/h$. These features greatly contrast those of an MBS or quasi-MBS, whose $P(V)$ curve displays a broad zero-bias dip and is consistently below $2e^3/h$. This protocol can be practically implemented in a variety of MBS candidate platforms using an electrode or STM tip as a probe. △ Less

Submitted 15 September, 2023; v1 submitted 16 January, 2023; originally announced January 2023.

Comments: 7 pages, 5 figures, and 1 table in the main text; 12 pages, 11 figures, and 4 tables in the Supplemental Material

Journal ref: Physical Review B 108, L121407 (2023)

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)

In situ tuning of dynamical Coulomb blockade on Andreev bound states in hybrid nanowire devices

Authors: Shan Zhang, Zhichuan Wang, Dong Pan, Zhaoyu Wang, Zonglin Li, Zitong Zhang, Yichun Gao, Zhan Cao, Gu Zhang, Lei Liu, Lianjun Wen, Ran Zhuo, Dong E. Liu, Ke He, Runan Shang, Jianhua Zhao, Hao Zhang

Abstract: Electron interactions in quantum devices can exhibit intriguing phenomena. One example is assembling an electronic device in series with an on-chip resistor. The quantum laws of electricity of the device is modified at low energies and temperatures by dissipative interactions induced by the resistor, a phenomenon known as dynamical Coulomb blockade (DCB). The DCB strength is usually non-adjustable… ▽ More Electron interactions in quantum devices can exhibit intriguing phenomena. One example is assembling an electronic device in series with an on-chip resistor. The quantum laws of electricity of the device is modified at low energies and temperatures by dissipative interactions induced by the resistor, a phenomenon known as dynamical Coulomb blockade (DCB). The DCB strength is usually non-adjustable in a fixed environment defined by the resistor. Here, we design an on-chip circuit for InAs-Al hybrid nanowires where the DCB strength can be gate-tuned in situ. InAs-Al nanowires could host Andreev or Majorana zero-energy states. This technique enables tracking the evolution of the same state while tuning the DCB strength from weak to strong. We observe the transition from a zero-bias conductance peak to split peaks for Andreev zero-energy states. Our technique opens the door to in situ tuning interaction strength on zero-energy states. △ Less

Submitted 12 December, 2023; v1 submitted 14 November, 2022; originally announced November 2022.

Journal ref: Phys. Rev. B 108, 235416 (2023)

Electrostatic effects of the MnBi2Te4-superconductor hetero-structures in chiral Majorana search

Authors: Li Chen, Zhan Cao, Ke He, Xin Liu, Dong E. Liu

Abstract: The realization of chiral Majorana modes is a challenging task. We aim to comprehend the phase diagrams and parameter control capabilities of the actual devices used in the chiral Majorana search. Beyond the well-known minimal models, we develop a numerical simulation scheme using a self-consistent Schrodinger-Poisson approach to study, as an example, the MnBi2Te4 thin film coupled to an s-wave su… ▽ More The realization of chiral Majorana modes is a challenging task. We aim to comprehend the phase diagrams and parameter control capabilities of the actual devices used in the chiral Majorana search. Beyond the well-known minimal models, we develop a numerical simulation scheme using a self-consistent Schrodinger-Poisson approach to study, as an example, the MnBi2Te4 thin film coupled to an s-wave superconductor. We show that both the superconducting proximity effect and the tunability of the chemical potential for the topological surface states are significantly influenced by the gate-induced electrostatic potential. This complicates the implementation in experiments, and the actual topological region will be narrowed in stark contrast to those predicted in the previous minimal models. Nevertheless, we demonstrate that the chiral Majorana mode still exists in a wide range of experimental parameters with practical tunability. △ Less

Submitted 13 April, 2023; v1 submitted 3 November, 2022; originally announced November 2022.

Comments: 11 pages, 9 figures

Journal ref: Phys. Rev. B 107, 165405 (2023)

Theoretical proposal to obtain strong Majorana evidence from scanning tunneling spectroscopy of a vortex with a dissipative environment

Authors: Gu Zhang, Chuang Li, Geng Li, Can-Li Song, Xin Liu, Fu-Chun Zhang, Dong E. Liu

Abstract: It is predicted that a vortex in a topological superconductor contains a Majorana zero mode (MZM). The confirmative Majorana signature, i.e., the $2e^2/h$ quantized conductance, however is easily sabotaged by unavoidable interruptions, e.g. instrument broadening, non-Majorana signal, and extra particle channels. We propose to avoid the signal interruption by introducing disorder-induced dissipatio… ▽ More It is predicted that a vortex in a topological superconductor contains a Majorana zero mode (MZM). The confirmative Majorana signature, i.e., the $2e^2/h$ quantized conductance, however is easily sabotaged by unavoidable interruptions, e.g. instrument broadening, non-Majorana signal, and extra particle channels. We propose to avoid the signal interruption by introducing disorder-induced dissipation that couples to the tip-sample tunneling. With dissipation involved, we highlight three features, each of which alone can provide a strong evidence to identify MZM. Firstly, dissipation suppresses a finite-energy Caroli-de Gennes-Matricon (CdGM) conductance peak into a valley, while it does not split MZM zero-bias conductance peak. Secondly, we predict a dissipation-dependent scaling feature of the zero-bias conductance peak. Thirdly, the introduced dissipation manifests the MZM signal by suppressing non-topological CdGM modes. Importantly, the observation of these features does not require a quantized conductance value $2e^2/h$. △ Less

Submitted 9 July, 2023; v1 submitted 28 September, 2022; originally announced September 2022.

Comments: We express our gratitude to Dr. Odobesko for bringing to our attention an intriguing and pertinent experimental paper: Phys. Rev. B 102, 174502 (2020), which is Ref. [71] of the current arXiv version

Journal ref: Phys. Rev. B 107, 19541 (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)

Recent progress on Majorana in semiconductor-superconductor heterostructures--Engineering and detection

Authors: Zhan Cao, Shumeng Chen, Gu Zhang, Dong E. Liu

Abstract: Majorana zero modes (MZMs) are exotic excitations (in condensed matter systems) that have potential applications in topological quantum computation. Though MZMs have been predicted on many platforms, their existence of them is still under debate. In this paper, we review the recent progress of engineering and detecting MZMs in semiconductor-superconductor heterostructures. We also briefly review t… ▽ More Majorana zero modes (MZMs) are exotic excitations (in condensed matter systems) that have potential applications in topological quantum computation. Though MZMs have been predicted on many platforms, their existence of them is still under debate. In this paper, we review the recent progress of engineering and detecting MZMs in semiconductor-superconductor heterostructures. We also briefly review the protocols of implementing topological quantum computation by hybrid semiconductor-superconductor nanowires. △ Less

Submitted 13 April, 2023; v1 submitted 14 June, 2022; originally announced June 2022.

Comments: Invited review in Science China Physics Mechanics & Astronomy, with 7 figures, 15 pages

Journal ref: SCIENCE CHINA Physics, Mechanics & Astronomy, 66, 6: 267003 (2023)

Probing electron-hole weights of an Andreev bound state by transient currents

Authors: Zhan Cao, Gu Zhang, Hao Zhang, Wan-Xiu He, Chuanchang Zeng, Ke He, Dong E. Liu

Abstract: Andreev bound states (ABSs) are localized quantum states that contain both electron and hole components. They ubiquitously reside in inhomogeneous superconducting systems. Following theoretical analysis, we propose to probe the electron-hole weights of an ABS via a local tunneling measurement that detects the transient current under a steplike pulse bias. With our protocol, the ABS energy level ca… ▽ More Andreev bound states (ABSs) are localized quantum states that contain both electron and hole components. They ubiquitously reside in inhomogeneous superconducting systems. Following theoretical analysis, we propose to probe the electron-hole weights of an ABS via a local tunneling measurement that detects the transient current under a steplike pulse bias. With our protocol, the ABS energy level can also be obtained from peaks of the Fourier spectrum of the transient current. Our protocol can be applied to detect robust zero-energy Majorana bound states (MBSs), which have equal electron-hole weights, in candidate platforms where local tunneling spectroscopy measurement is possible. In the 1D Majorana nanowire model, we numerically calculate the electron-hole weights for different types of low-energy bound states, including ABSs, quasi-MBSs, and MBSs. △ Less

Submitted 19 August, 2022; v1 submitted 10 June, 2022; originally announced June 2022.

Comments: 14 pages, 5 figures

Journal ref: Physical Review B 106, 075416 (2022)

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

Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$

Authors: Zhaoyu Wang, Huading Song, Dong Pan, Zitong Zhang, Wentao Miao, Ruidong Li, Zhan Cao, Gu Zhang, Lei Liu, Lianjun Wen, Ran Zhuo, Dong E. Liu, Ke He, Runan Shang, Jianhua Zhao, Hao Zhang

Abstract: Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at $2e^2/h$ at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close t… ▽ More Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at $2e^2/h$ at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to $2e^2/h$, mostly within $5\%$ tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence of disorder and quantum dots, our result constitutes a step forward towards establishing Majorana zero modes. △ Less

Submitted 14 October, 2022; v1 submitted 13 May, 2022; originally announced May 2022.

Comments: Raw data and processing codes within this paper are available at https://doi.org/10.5281/zenodo.6546974

Journal ref: Phys. Rev. Lett. 129, 167702 (2022)

Large Andreev bound state zero bias peaks in a weakly dissipative environment

Authors: Zhichuan Wang, Shan Zhang, Dong Pan, Gu Zhang, Zezhou Xia, Zonglin Li, Donghao Liu, Zhan Cao, Lei Liu, Lianjun Wen, Dunyuan Liao, Ran Zhuo, Yongqing Li, Dong E. Liu, Runan Shang, Jianhua Zhao, Hao Zhang

Abstract: We study Andreev bound states in hybrid InAs-Al nanowire devices. The energy of these states can be tuned to zero by gate voltage or magnetic field, revealing large zero bias peaks (ZBPs) near 2e^2/h in tunneling conductance. Probing these large ZBPs using a weakly dissipative lead reveals non-Fermi liquid temperature (T) dependence due to environmental Coulomb blockade (ECB), an interaction effec… ▽ More We study Andreev bound states in hybrid InAs-Al nanowire devices. The energy of these states can be tuned to zero by gate voltage or magnetic field, revealing large zero bias peaks (ZBPs) near 2e^2/h in tunneling conductance. Probing these large ZBPs using a weakly dissipative lead reveals non-Fermi liquid temperature (T) dependence due to environmental Coulomb blockade (ECB), an interaction effect from the lead acting on the nanowire junction. By increasing T, these large ZBPs either show a height increase or a transition from split peaks to a ZBP, both deviate significantly from non-dissipative devices where a Fermi-liquid T dependence is revealed. Our result demonstrates the competing effect between ECB and thermal broadening on Andreev bound states. △ Less

Submitted 18 February, 2022; originally announced February 2022.

Comments: Raw data and processing codes are available at https://doi.org/10.5281/zenodo.6123849

Journal ref: Phys. Rev. B 106, 205421 (2022)

Double Fu-teleportation and anomalous Coulomb blockade in a Majorana-hosted superconducting island

Authors: Yiru Hao, Gu Zhang, Donghao Liu, Dong E. Liu

Abstract: We study the temperature dependence of Coulomb Blockade peak conductance based on a Majorana-hosted superconducting island. In the low-temperature regime, we discover a coherent double Fu-teleportation (FT) process, where any independent tunneling process always involves two coherent FTs; and we also find an anomalous universal scaling behavior, which shows a transition from a [max(T,eV)]^6 to a [… ▽ More We study the temperature dependence of Coulomb Blockade peak conductance based on a Majorana-hosted superconducting island. In the low-temperature regime, we discover a coherent double Fu-teleportation (FT) process, where any independent tunneling process always involves two coherent FTs; and we also find an anomalous universal scaling behavior, which shows a transition from a [max(T,eV)]^6 to a [max(T,eV)]^3 conductance behavior as increasing energy scale. In the high-temperature regime, using the familiar rate equation method, we find that the conductance is proportional to the reciprocal of the temperature and shows a non-monotonic temperature-dependence. Both the anomalous power-law behavior and non-monotonic temperature-dependence can be distinguished from the conductance peak in the traditional Coulomb block, and therefore, serve as a hallmark for the non-local transport in the topological superconducting island. △ Less

Submitted 27 January, 2022; v1 submitted 20 January, 2022; originally announced January 2022.

Comments: 11 pages 3 figures, minor changes of the main text and references

Journal ref: Nature Communications 13, 6699 (2022)