Numerical Experiments with Parameter Setting of Trotterized Quantum Phase Estimation for Quantum Hamiltonian Ground State Computation
This work provides practical tuning guidelines for QPE on small quantum systems, but the findings are incremental and limited to specific small-scale models.
The authors numerically study the parameter settings of Trotterized Quantum Phase Estimation (QPE) for computing ground-state energies of small quantum Heisenberg spin glasses (3 qubits). They find that QPE sampling of the optimal digitized phase converges to a fixed rate, leading to diminishing returns even when Trotter error is high.
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.