量子线性系统求解器的迭代细化分析
An analysis of iterative refinement for quantum linear system solvers
- Pacific Northwest National Laboratory（太平洋西北国家实验室）
- Lehigh University（利哈伊大学）
- University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
- Quantum Science Institute（量子科学研究所）
- University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种迭代细化框架，通过求解一系列相关线性系统，在仅使用固定精度量子子程序的情况下，保持量子线性系统算法对逆误差容限的多对数依赖，并最终获得高精度解的经典描述，实验验证其有效性和鲁棒性。
AI中文摘要：
我们提出并分析了一种迭代细化（IR）框架，用于改善结合量子线性系统算法（QLSA）与量子态层析成像的算法的精度依赖性。现有的QLSA在制备编码解的量子态时，对逆误差容限实现多对数依赖，但通过层析成像提取此类态的经典描述通常引入对目标精度的多项式依赖。为在整个过程中保持对逆误差容限的多对数依赖，我们开发了一种IR方案，该方案求解一系列相关的线性系统以逐步细化解，同时仅需要固定精度的量子子程序，最终获得高精度解的经典描述。我们在三种输入模型下分析所提出的框架：量子读/经典写随机存取存储器（QRAM）、酉算子线性组合（LCU）以及稀疏访问预言机。我们通过量子模拟器和真实量子硬件上的数值实验评估所提出的方案。结果表明，迭代细化有效提高了解的精度，并对硬件噪声表现出鲁棒性。
英文摘要：
We present and analyze an iterative refinement (IR) framework for improving the precision dependence of algorithms that combine a quantum linear system algorithm (QLSA) with quantum state tomography. Existing QLSAs achieve polylogarithmic dependence on the inverse error tolerance to prepare a quantum state encoding the solution, but extracting a classical description of such a state via tomography typically introduces a polynomial dependence on the target precision. To retain polylogarithmic dependence in the inverse error tolerance throughout the entire process, we develop an IR scheme that solves a sequence of related linear systems to progressively refine the solution while requiring only fixed-precision quantum subroutines, finally obtaining a classical description of a high-precision solution. We analyze the proposed framework under three input models: quantum-read/classical-write RAM (QRAM), linear combinations of unitaries (LCU), and sparse-access oracles. We evaluate the proposed scheme through numerical experiments on both quantum simulators and real quantum hardware. The results demonstrate that iterative refinement efficiently improves the precision of the solution and exhibits robustness to hardware noise.
