容错量子动力学模拟中的量子-经典交叉
Quantum-classical crossover in fault-tolerant quantum dynamics simulation
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中文总结 AI 辅助
研究在现实硬件条件下量子多体动力学的量子-经典交叉，引入可扩展容错框架，结合相干可观测量估计与非克利福德旋转实现，通过与经典算法对比，得出不同错误率下的运行时间等结果，为量子优势建立途径并确定工程目标。
中文摘要 AI 辅助
虽然量子计算机有望解决经典计算难以处理的问题，但确定容错量子计算在实际应用中超越最佳经典算法的点仍然是一个重大挑战。本文在现实硬件条件下为量子多体动力学建立了具体的量子-经典交叉。引入了一个可扩展的容错框架，将相干可观测量估计与非克利福德旋转的时空高效实现相结合，抑制限制现有部分容错方法的残余逻辑错误。与先进的张量网络和变分蒙特卡罗算法的基准测试揭示了在适度系统规模下混合场伊辛动力学的具体交叉。对于物理错误率\(p = 10^{-3}\)，100 个格点的 1D 系统的容错模拟需要约 2 小时和\(3.7×10^5\)个物理量子比特，而张量网络方法需要约 100 年。对于 2D 模型，量子运行时间在几分钟内。物理错误率\(p = 10^{-4}\)导致量子比特数和运行时间至少降低一个数量级。量子运行时间的减少源于改进的旋转态注入以及量子纠错和可观测量估计协议的协同设计，共同抑制逻辑错误积累并减少采样开销。结果为实现实际量子优势建立了可扩展途径，并为未来容错架构确定了定量工程目标。
英文摘要
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.
