Numerical Experiments with Parameter Setting of Trotterized Quantum Phase Estimation for Quantum Hamiltonian Ground State Computation
Abstract
We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected quantum Heisenberg spin glass model. We consider (classical simulations of) QPE circuit computations on relatively small quantum Hamiltonians ( qubits) with up to phase bits of precision, using up to Trotter order . We systematically study the inputs of QPE, specifically time evolution, Trotter order, Trotter steps, and initial state, and illustrate how these inputs practically determine how QPE operates. From this we outline a coherent set of quantum algorithm input and tuning guidelines. One of the notable properties we characterize is that QPE sampling of the optimal digitized phase converges to a fixed rate. This results in strong diminishing returns of optimal phase sampling rates which can occur when the Trotter error is surprisingly high.
Cite
@article{arxiv.2602.22349,
title = {Numerical Experiments with Parameter Setting of Trotterized Quantum Phase Estimation for Quantum Hamiltonian Ground State Computation},
author = {Elijah Pelofske and Stephan Eidenbenz},
journal= {arXiv preprint arXiv:2602.22349},
year = {2026}
}