One of the most promising applications of quantum computers is to simulate physical systems, leveraging their inherent quantum behavior to achieve an advantage over classical computation. In this work, we present a noise-tolerant Hamiltonian simulation algorithm for ground-state energy estimation. Our method surmounts stochastic sampling limitations to estimate expectation values. It is based on an adaptive sequence of fuzzy bisection searches to estimate the ground state energy digit by digit, with a trade-off between increasing the simulation time and decreasing the absolute error rate. It builds upon the Quantum Eigenvalue Transformation of Unitary Matrices (QETU) algorithm, and it delivers good approximations in simulations with local, two-qubit gate depolarizing probability up to 1e-3, specifically for Hamiltonians that anti-commute with a Pauli string. To demonstrate the key results in this work, we ran simulations with different system Hamiltonians, system sizes, and time evolution encoding methods on classical computers using Qiskit. We compare the performance with other existing methods and show that we can consistently achieve two to three orders of magnitude improvement in the absolute error rate.

翻译：量子计算机最有前景的应用之一是模拟物理系统，利用其固有的量子行为来实现对经典计算的优越性。本文提出一种用于基态能量估计的噪声容忍哈密顿量模拟算法。该方法克服了随机采样的局限性以估算期望值，其核心基于自适应模糊二分搜索序列，通过逐位估计基态能量，并在增加模拟时间与降低绝对误差率之间取得平衡。该算法以量子特征值变换算法（QETU）为基础，能够在局部双量子比特门退极化概率高达1e-3的模拟中提供良好近似，尤其适用于与泡利算符串反对易的哈密顿量。为验证本文关键结果，我们利用Qiskit在经典计算机上对不同系统哈密顿量、系统规模和含时演化编码方法进行了模拟。与现有其他方法相比，我们的算法在绝对误差率上持续实现了两到三个数量级的提升。