Quantum Orbital Minimization Method for Excited States Calculation on Quantum Computer

TL;DR

The paper introduces a hybrid quantum-classical algorithm, qOMM, for efficiently computing ground and excited states of Hermitian operators, demonstrating advantages over existing methods in simulations.

Contribution

It presents the quantum orbital minimization method (qOMM), a novel hybrid algorithm that improves excited state calculations on quantum computers with better convergence and shallower circuits.

Findings

qOMM successfully finds excited states of molecules and a toy model.

qOMM is less prone to local minima compared to existing methods.

qOMM achieves convergence with shallower ansatz circuits.

Abstract

We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parameterized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts classical optimizer to minimize the objective function with respect to parameters in ansatz circuits. The objective function has orthogonality implicitly embedded, which allows qOMM to apply a different ansatz circuit to each reference state. We carry out numerical simulations that seek to find excited states of the $\text{H}_{2}$, $\text{LiH}$, and a toy model consisting of 4 hydrogen atoms arranged in a square lattice in the STO-3G basis and UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.