A variational eigenvalue solver on a quantum processor

TL;DR

This paper introduces a variational eigenvalue solver on a quantum processor that reduces coherence time requirements, enabling practical quantum chemistry calculations with current quantum hardware.

Contribution

It presents a new variational algorithm combining ansatz-based state preparation with classical optimization, demonstrated on a photonic quantum processor for molecular energy estimation.

Findings

Successfully calculated ground state energy of He-H+ within chemical accuracy.

Reduced coherence time requirements compared to quantum phase estimation.

Feasibility demonstrated on a small-scale photonic quantum processor.

Abstract

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm can efficiently find the eigenvalue of a given eigenvector but requires fully coherent evolution. We present an alternative approach that greatly reduces the requirements for coherent evolution and we combine this method with a new approach to state preparation based on ans\"atze and classical optimization. We have implemented the algorithm by combining a small-scale photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry: calculating the ground state molecular energy for He-H+, to within chemical accuracy. The proposed approach, by drastically reducing the coherence time requirements, enhances the potential of the quantum resources available today and in the near future.