早期容错量子计算时代的统计相位估计与变异量子求解器的对比

Ming-Zhi Chung, Andreas Thomasen, Henry Liao, Ryosuke Imai
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引用次数: 0

摘要

在这篇综述中,我们概述了在早期 FTQC(EFTQC)时代提出的应用。从 EFTQC 器件的纠错架构开始,我们首先回顾了最近开发的时空高效模拟旋转(STAR)架构(cite{akahoshiPartiallyFaultTolerantQuantum2024}),这是一种局部容错的纠错架构。然后,我们回顾了 EFTQC 算法的要求。特别是,我们研究了一类被称为统计相位估计算法(SPE)的基态能量估计(GSEE)算法。我们特别关注了两种SPE类型的算法,即Lin和Tong(LT22)基于阶跃函数滤波器的变体(LT22)和高斯滤波器(Gaussian Filter)。在后者的基础上,我们引入了高斯拟合算法,该算法与 (cite{Wang:2022gxu}相比使用了另一种后处理程序。最后,我们系统地模拟了上述算法和变分量子求解器(VQE),使用的是具有不同射数的 1-uCJ 解析。最重要的是,我们基于 STAR 架构进行了噪声模拟。我们发现,当物理误差率足够低时,在估算STO-3G 基础上的 4 量子位 $H_2$Hamiltonian 的基态能量时,SPE 比 VQE 更有优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Contrasting Statistical Phase Estimation with the Variational Quantum Eigensolver in the era of Early Fault Tolerant Quantum Computation
In this review, we give an overview of the proposed applications in the early-FTQC (EFTQC) era. Starting from the error correction architecture for EFTQC device, we first review the recently developed space-time efficient analogue rotation (STAR) architecture \cite{akahoshiPartiallyFaultTolerantQuantum2024}, which is a partially fault-tolerant error correction architecture. Then, we review the requirements of an EFTQC algorithm. In particular, the class of ground state energy estimation (GSEE) algorithm known as the statistical phase estimation algorithm (SPE) is studied. We especially cast our attention on two SPE-type algorithms, the step-function filter-based variant by Lin and Tong (LT22) \cite{Lin:2021rwb} and Gaussian Filter \cite{Wang:2022gxu}. Based on the latter, we introduce the Gaussian Fitting algorithm, which uses an alternative post-processing procedure compared to \cite{Wang:2022gxu}. Finally, we systematically simulate the aforementioned algorithms and Variational Quantum Eigensolver (VQE) using the 1-uCJ ansatz with different shot counts. Most importantly, we perform noisy simulations based on the STAR architecture. We find that for estimating the ground state energy of the 4-qubit $H_2$ Hamiltonian in the STO-3G basis, SPE becomes more advantageous over VQE when the physical error rate is sufficiently low.
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