One of the most promising applications of quantum computers is to simulate quantum mechanical systems and deliver an advantage to classical computation by leveraging their inherent quantum behaviour. In this work, we present a new approach to achieve a noise tolerant Hamiltonian simulation algorithm for ground state energy estimation which also surmounts stochastic limitations most of its counterparts face. This algorithm is based on an adaptive set of fuzzy bisection searches to estimate the ground state energy digit by digit that can get to any arbitrary target precision. It builds upon the Quantum Eigenvalue Transformation of Unitary Matrices (QETU) algorithm and it delivers good approximations in simulations with quantum depolarizing probability up to 1e-3, particularly for the Transverse-Field Ising Model (TFIM). We ran simulations with different system Hamiltonians, system sizes and time evolution encoding methods on IBM Qiskit and we demonstrate the key results in this work, as well as compare the performance with other existing methods.

翻译：量子计算机最有前景的应用之一是利用其固有的量子行为模拟量子力学系统，并在经典计算中实现优势。本研究提出了一种新的噪声容忍哈密顿量模拟算法，用于基态能量估计，该算法同时克服了同类方法大多面临的随机性限制。该算法基于一组自适应模糊二分搜索，逐位估计基态能量，可达到任意目标精度。它建立在量子矩阵西变换算法(QETU)之上，在量子退极化概率高达1e-3的模拟中都能提供良好的近似结果，特别是对于横向场伊辛模型(TFIM)。我们使用IBM Qiskit对不同系统哈密顿量、系统大小和时间演化编码方法进行了模拟，展示了本研究的关键成果，并与其他现有方法进行了性能比较。