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

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.