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 ($3$ 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.

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Numerical Analysis (math.NA)

arXiv:2602.22349 [quant-ph]

(or arXiv:2602.22349v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.22349 Focus to learn more arXiv-issued DOI via DataCite

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