arXiv subjects

Keming He

Publications and source records attributed to Keming He.

10 recordsLinked to original sources

arXiv2026

QECert: Formal Foundations for Quantum Error-Correction Theory in Lean

Quantum error correction provides the mathematical basis for protecting quantum information against noise. Existing formalizations have established foundations for stabilizer codes and code verification. However, a systematic formal treatment of the asymptotic constructions and fundamental limitations that underpin scalable quantum error correction is still needed. We present QECert, a Lean library providing reusable formal foundations for these theoretical questions. It connects quantum error-correction criteria, stabilizer and Calderbank-Shor-Steane codes, and algebraic and homological constructions within a common framework. Asymptotically good quantum low density parity check codes provide the principal case study. We formalize constructions and asymptotic parameter theorems spanning hypergraph products, balanced products, lifted products, and quantum Tanner codes. Further developments cover Bravyi-Poulin-Terhal bounds and related locality restrictions, constant overhead magic state distillation, and energy barriers and storage errors for quantum memories. QECert establishes a reusable formal foundation for studying the capabilities, resource requirements, and fundamental limitations of quantum error correction, supporting systematic verification and further development of its theory.

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arXiv2026

Nearly Optimal T-Count for Symmetry-Based Quantum State Purification

Protecting quantum information from noise is essential for reliable quantum computation and quantum memories. Quantum state purification addresses this challenge by processing multiple noisy copies of an unknown quantum state to produce an output state of higher fidelity. Here we establish nearly tight upper and lower bounds on the non-Clifford resources required to implement the symmetric-projection purification protocol. For $n$ copies of a $d$-dimensional system, we construct a Clifford+T circuit that block-encodes the symmetric projector with operator-norm error at most $ε$ using $\widetilde{O}(n)$ T gates, where the tilde-$O$ notation suppresses polylogarithmic factors in $n$, $d$, and $1/ε$. Conversely, using stabilizer nullity, we prove that any Clifford+T implementation of such a block encoding with error $ε<\frac{1}{2}\sqrt{1-1/n}$ requires at least $2n-2$ T gates, even allowing arbitrary positive normalization and clean stabilizer ancillas. Taken together, these results establish the nearly optimal scaling of non-Clifford cost with the number of copies and uncover the fundamental resource requirements for coherent symmetry projection in quantum state purification.

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arXiv2026

Quantum Compiler Design for Fault-Tolerant Quantum Computing

Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding. This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.

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arXiv2026

Logical Entangling with Phantom Codes in Hypergraph Products

Logical entangling gates are a major source of physical spacetime overhead in fault-tolerant quantum computation. Phantom codes reduce this cost by implementing every ordered in-block logical CNOT through physical qubit permutations and Pauli-frame updates. Whether this mechanism can coexist with the low-weight stabilizer structure of qLDPC codes is a central question for low-overhead fault-tolerant architectures. We give a deterministic answer within binary CSS hypergraph product (HGP) codes. Up to natural equivalences, the simplex-repetition family is the unique HGP family satisfying the phantom condition. We then evaluate this family under circuit-level noise in logical GHZ-state preparation and Trotterized many-body quantum simulation. The codes retain low-weight stabilizer checks and yield concrete advantages over rotated surface-code baselines in both benchmarks. Reconfigurable neutral-atom arrays offer a natural setting for this approach, supporting nonlocal qLDPC operations while enabling in-block logical CNOTs without additional physical operations. Together, these results make precise how permutation-based logical entangling constrains code design within the HGP framework, demonstrate the circuit-level benefits of the unique family, and guide the search for phantom qLDPC families with better asymptotic parameters for low-overhead fault tolerance on neutral-atom hardware.

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arXiv2026

A Nonstabilizerness Resource Law for Universal Quantum State Purification

Quantum state purification aims to recover higher-fidelity quantum states from multiple noisy copies and is a fundamental primitive for quantum information processing. Magic resources enable operations beyond classically simulable dynamics and are central to universal fault-tolerant quantum computation. Recent no-go results show that classically simulable operations cannot achieve a nontrivial universal fidelity gain. This motivates a quantitative theory of the magic required for purification at prescribed success probability and target fidelity. For universal purification with two input copies, we prove an exact linear mana law in odd dimensions and a two-sided linear robustness law for multi-qubit systems, which becomes exact for a single qubit. We also identify an explicit successful purification map that makes the tradeoff transparent. These results establish universal purification as a task obeying a quantitative magic-fidelity law and link magic resources to error mitigation and fault-tolerant quantum information processing.

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arXiv2026

O3LS: Optimizing Lattice Surgery via Automatic Layout Searching and Loose Scheduling

Toward the large-scale, practical realization of quantum computing, quantum error correction is essential. Among various quantum error-correcting codes, the surface code stands out as a leading candidate, and lattice surgery based on surface codes has emerged as a promising technique for fault-tolerant quantum computation (FTQC). However, implementing quantum algorithms using lattice surgery introduces both resource and time overhead. Existing approaches typically focus on large layout designs, with compiler passes aimed primarily at optimizing time overhead. This often overlooks the trade-off between rotation bottlenecks and movement distance, which leads to inefficient resource utilization and prevents further reduction of the quantum computation failure rate. To address these challenges, we introduce O3LS, a framework for optimizing lattice surgery through automatic layout search and loose scheduling. O3LS achieves an optimal balance by automatically generating squeezed data layouts to reduce space requirements and employing loose scheduling algorithms combined with circuit synthesis techniques to reduce time overhead, thereby effectively minimizing overall logical error rates. Numerical results indicate that O3LS can reduce space overhead by 28.0% over standard layouts and 46.7% over sparse layouts without increasing the number of time steps, leading to suppression of logical error rates by up to 16% relative to larger data layout designs. O3LS can also achieve time overhead reductions of 36.07% and 24.76% in compact and standard data layout designs, respectively. It suppresses logical error rates by up to an order of magnitude compared to prior compilers that focus primarily on maximizing parallelism.

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arXiv2026

Block Coordinate Descent for Dynamic Portfolio Optimization on Finite-Precision Coherent Ising Machines

Coherent Ising machines (CIMs) have emerged as specialized quantum hardware for large-scale combinatorial optimization. However, for large instances that remain challenging for classical methods, some platforms support only finite-precision inputs, and the required scaling and quantization can degrade solution quality. Dynamic portfolio optimization (DPO) can be formulated as a quadratic unconstrained binary optimization (QUBO) problem, but large instances are especially vulnerable to precision loss under global scaling. We propose a block coordinate descent method that decomposes the DPO model along the time dimension and iteratively solves compact time-block subproblems on the device. Experiments on finite-precision CIM hardware show that the method enables these instances to be solved under hardware precision limits, yields portfolios competitive with classical benchmark solvers, and reduces runtime through fast CIM solution of the resulting subproblems. These results demonstrate the promise of finite-precision CIMs as a practical and scalable approach to structured large-scale combinatorial optimization.

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arXiv2025

No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations

Quantum state purification, a process that aims to recover a state closer to a system's principal eigenstate from multiple copies of an unknown noisy quantum state, is crucial for restoring noisy states to a more useful form in quantum information processing. Fault-tolerant quantum computation relies on stabilizer operations, which are classically simulable protocols critical for error correction but inherently limited in computational power. In this work, we investigate the limitations of classically simulable operations for quantum state purification. We demonstrate that while certain classically simulable operations can enhance fidelity for specific noisy state ensembles, they cannot achieve universal purification. We prove that neither deterministic nor probabilistic protocols using only classically simulable operations can achieve universal purification of two-copy noisy states for qubit systems and all odd dimensions. We further extend this no-go result of state purification using three and four copies via numerical solutions of semidefinite programs. Our findings highlight the indispensable role of non-stabilizer resources and the inherent limitations of classically simulable operations in quantum state purification, emphasizing the necessity of harnessing the full power of quantum operations for more robust quantum information processing.

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arXiv2025

Virtual Quantum Markov Chains

Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept of virtual quantum Markov chains (VQMCs), focusing on scenarios where subsystems retain classical information about global systems from measurement statistics. As a generalization of quantum Markov chains, VQMCs characterize states where arbitrary global shadow information can be recovered from subsystems through local quantum operations and measurements. We present an algebraic characterization for virtual quantum Markov chains and show that the virtual quantum recovery is fully determined by the block matrices of a quantum state on its subsystems. Notably, we find a distinction between two classes of tripartite entanglement by showing that the W state is a VQMC while the GHZ state is not. Furthermore, we introduce the virtual non-Markovianity to quantify the non-Markovianity of a given quantum state, which also assesses the optimal sampling overhead for virtually recovering this state. Our findings elucidate distinctions between quantum Markov chains and virtual quantum Markov chains, extending our understanding of quantum recovery to scenarios prioritizing classical information from measurement statistics.

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arXiv2025

Hypothesis testing of symmetry in quantum dynamics

Symmetry plays a crucial role in quantum physics, dictating the behavior and dynamics of physical systems. In this paper, we develop a hypothesis-testing framework for quantum dynamics symmetry using a limited number of queries to the unknown unitary operation and establish the quantum max-relative entropy lower bound for the type-II error. We construct optimal ancilla-free protocols that achieve optimal type-II error probability for testing time-reversal symmetry (T-symmetry) and diagonal symmetry (Z-symmetry) with limited queries. Contrasting with the advantages of indefinite causal order strategies in various quantum information processing tasks, we show that parallel, adaptive, and indefinite causal order strategies have equal power for our tasks. We establish optimal protocols for T-symmetry testing and Z-symmetry testing for 6 and 5 queries, respectively, from which we infer that the type-II error exhibits a decay rate of $\mathcal{O}(m^{-2})$ with respect to the number of queries $m$. This represents a significant improvement over the basic repetition protocols without using global entanglement, where the error decays at a slower rate of $\mathcal{O}(m^{-1})$.

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