Witnessing eigenstates for quantum simulation of Hamiltonian spectra

TL;DR

This paper introduces a quantum method combining variational techniques and phase estimation to efficiently approximate Hamiltonian eigenvalues, validated on a silicon photonic chip with high fidelity and precision, advancing quantum chemistry simulations.

Contribution

The paper presents a novel quantum approach using an eigenstate witness to accurately estimate eigenvalues of Hamiltonians, including excited states, on a programmable photonic platform.

Findings

Achieved >99% fidelity in experimentally finding eigenstates.

Estimated eigenvalues with 32-bit precision.

Demonstrated scalability through numerical simulations.

Abstract

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.