Bootstrap Embedding on a Quantum Computer

TL;DR

This paper introduces a quantum-enhanced bootstrap embedding method for molecular electronic structure calculations, leveraging quantum algorithms to achieve quadratic speedups and improved fragment boundary solutions.

Contribution

It extends classical bootstrap embedding to quantum computers, enabling efficient large-molecule electronic structure solutions with quantum subroutines and full density matrix matching.

Findings

Quadratic speedup over classical algorithms.

Ability to match full density matrices at fragment boundaries.

Potential for use with small, near-term quantum computers.

Abstract

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.