Numerical Experiments with Parameter Setting of Trotterized Quantum Phase Estimation for Quantum Hamiltonian Ground State Computation

TL;DR

This paper numerically investigates how parameter choices in Trotterized Quantum Phase Estimation affect the accuracy and efficiency of computing ground-state energies of small quantum Hamiltonians, providing practical guidelines.

Contribution

It systematically analyzes the impact of Trotterization parameters on QPE performance and characterizes convergence properties of phase sampling in quantum simulations.

Findings

QPE sampling of the optimal phase converges to a fixed rate.

High Trotter error can cause diminishing returns in phase sampling.

Guidelines for tuning QPE parameters are proposed.

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 ($3$ qubits) with up to $10$ phase bits of precision, using up to Trotter order $10$. 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.