Noise-Tolerant Quantum Algorithm for Ground State Energy Estimation

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.