Minimizing Trotter Approximation Error in Quantum Phase Estimation Using Genetic Algorithm

A key application of quantum computing is solving the electronic problem using Quantum Phase Estimation (QPE). The Trotter Approximation (TA) is one of the techniques used in QPE for encoding the Hamiltonian on a quantum computer. In TA, a Hamiltonian is partitioned into easily diagonalizable fragments. However, there is an error introduced in the unitary evolution operator when TA is applied. Different partitionings of a Hamiltonian and the ordering of the fragments yield different TA errors. In this work, we propose a novel two-step algorithm to obtain a near-optimal ordering for a given partitioning of a Hamiltonian. We find that when we use the Qubit-Wise Commuting partitioning method for the electronic Hamiltonian of molecule <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{2}$</tex>, our algorithm is approximately 6 times faster than evaluating all possible orderings exhaustively.