行列式量子-量子蒙特卡洛：相干辅助场采样
Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling
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中文总结 AI 辅助
该研究提出DQ²MC量子算法，将DQMC核心的辅助场采样迁移至量子计算机，消除马尔可夫链，电路深度更优，其费米子符号问题成本与量子弱值后选择开销精确对应。
中文摘要 AI 辅助
我们提出行列式量子-量子蒙特卡洛（DQ²MC），这是一种量子算法，它将行列式量子蒙特卡洛（DQMC）操作核心的辅助场采样与平均过程提升至量子计算机上执行。行列式预言机通过量子奇异值变换直接从单粒子作用量矩阵的块编码合成DQMC振幅，因此无需枚举、预计算或存储指数数量的哈伯德-斯特拉托诺维奇权重。由于固定辅助场时费米子是自由的，该构造完全在单粒子层面运行，需要O(log N_st)个系统量子比特，且无需Jordan-Wigner或Bravyi-Kitaev编码，其中N_st为时空体积。全量子协议将观测量转化为干涉振幅，完全消除了马尔可夫链及其自相关时间；混合量子-经典协议保留了恒定大小的活跃量子比特块，并用精确的热浴抽取取代了Metropolis-Hastings接受步骤，因此任意大小的簇更新均无拒绝，且仅在更新间传递经典信息，支持并行回火及量子处理器间的分布式执行。其电路深度随空间体积的扩展比经典DQMC更优，代价是后选择开销由最大目标概率精确决定：对于平滑分布为多项式开销，对于尖锐峰值分布为指数开销。最后，费米子符号问题背后的重权重估计子精确映射为量子弱值，使符号问题DQMC的指数成本与弱值提取的后选择开销精确对应。
英文摘要
We introduce determinant quantum-quantum Monte Carlo (DQ$^2$MC), a quantum algorithm that lifts the auxiliary-field sampling and averaging at the operational core of determinant quantum Monte Carlo onto a quantum computer. A determinant oracle synthesizes the DQMC amplitudes directly from a block encoding of the single-particle action matrix via quantum singular value transformations, so that the exponentially many Hubbard-Stratonovich weights are never enumerated, precomputed, or stored. Since the fermions are free for fixed auxiliary fields, the construction operates entirely at the single-particle level, requiring $O(\log N_{\mathrm{st}})$ system qubits and no Jordan-Wigner or Bravyi-Kitaev encoding, where $N_{\mathrm{st}}$ is the space-time volume. A full-quantum protocol makes observables interference amplitudes, eliminating the Markov chain and its autocorrelation time altogether; a hybrid quantum-classical protocol retains a constant-size active block of qubits and replaces the Metropolis-Hastings acceptance step with an exact heat-bath draw, so that cluster updates of any size are rejection-free, and passes only classical information between updates, admitting parallel tempering and distributed execution across quantum processors. The circuit-depth scales more favorably with spatial volume than classical DQMC, at the price of a post-selection overhead determined exactly by the largest target probability --- polynomial for smooth distributions, exponential for sharply peaked ones. Finally, the reweighting estimator underlying the fermion sign problem maps exactly onto a quantum weak value, placing the exponential cost of sign-problematic DQMC in precise correspondence with the post-selection overhead of weak-value extraction.
发表机构
- Cornell University（康奈尔大学）
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