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Dong E. Liu

Publications and source records attributed to Dong E. Liu.

At least 19 recordsLinked to original sources
arXiv2026

Single-shot state preparation threshold: rigorous theorem and statistical mechanical mapping

Preparing logical codewords with a single round of noisy syndrome measurements can reduce the time overhead of fault-tolerant quantum computation. It remains unclear which structural properties of the code suffice to guarantee a threshold for single-shot state preparation. Here we prove that linear confinement suffices for a nonzero single-shot state-preparation threshold for CSS quantum low-density parity-check codes, in contrast to the common belief that soundness is necessary. When the distance is at least logarithmic, we prove that below nonzero local stochastic readout and data error thresholds, the logical error probability after a formal ideal final recovery is exponentially small and approaches zero when the code size approaches infinity. Under the stronger assumption of linear soundness, we show that the residual data error of the preparation protocol is local stochastic, directly allowing composition with other fault-tolerant gadgets. To investigate single-shot state-preparation threshold beyond the above assumptions, we further develop a statistical mechanical mapping that expresses the final logical error rate in terms of a classical partition function. We perform Monte Carlo simulations of this model for the three-dimensional toric code. The numerical results suggest that sublinear soundness can also support a single-shot state-preparation threshold.

quant-ph↗
arXiv2026

Fragility of Magic State Distillation under Imperfect Measurements

Magic state distillation (MSD) is the leading approach for producing the non-Clifford resources required for universal fault-tolerant quantum computation. Most prior analyses of MSD assume ideal projective stabilizer measurements, but this assumption becomes questionable on near-term hardware, where measurement fidelity is limited and large quantum error-correcting codes are unavailable. We consider imperfect measurements that are modelled as noisy projector controlled by \textit{measurement strength}, which can be regarded as inverse of measurement noise, and develop a general framework for analyzing MSD under imperfect stabilizer measurements. We focus on MSD protocols that are based on CSS codes with transversal non-Clifford gates, and show that MSD exhibits a measurement-strength threshold that is distinct from the previously known threshold on input-state error. When measurement strength is below a critical threshold, MSD loses its distillation power entirely; When measurement strength is above this threshold, distillation under imperfect measurements remains possible, but the asymptotic target states may deviate from the ideal magic states. In particular, this deviation is at most first-order biased. Moreover, we show that imperfect measurements with finite measurement strength reduces the distillation efficiency to linear, implying exponentially larger distillation overheads than in the ideal-measurement case. We further show that this fragility can be mitigated generally up to the code capacity of MSD protocols by choosing the stabilizer generators to measure in the \textit{standard form}. Our results reveal fundamental constraints imposed by imperfect measurements on MSD and provide guidance for designing more robust distillation protocols in realistic quantum hardware.

quant-ph↗
arXiv2026

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

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. These charge modulations become strongly enhanced at the vortex core and extend far into the vortex halo. 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 intertwined phenomena in iron-based superconductors.

cond-mat.supr-con↗
arXiv2026

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

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.

quant-ph↗
arXiv2026

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

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.

cond-mat.mes-hall↗
arXiv2026

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

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.

quant-ph↗
arXiv2026

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

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.

quant-ph↗
arXiv2026

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

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.

quant-ph↗
arXiv2026

Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes

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.

quant-ph↗
arXiv2026

Charge Density Wave Driven Topological Phase Transition in Vortices

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.

cond-mat.supr-con↗
arXiv2026

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

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.

quant-ph↗
arXiv2026

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

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.

quant-ph↗
arXiv2025

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

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.

cond-mat.mes-hall↗
arXiv2025

From Magic State Distillation to Dynamical Systems

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.

quant-ph↗
arXiv2025

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

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.

quant-ph↗
arXiv2025

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

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.

quant-ph↗
arXiv2025

Detecting entanglement with transport measurement in weakly interacting and fluctuating systems

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.

cond-mat.mes-hall↗
arXiv2025

Protocol for detecting the nonlocality of the multi-Majorana Systems

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.

quant-ph↗