Doubling the Size of Quantum Simulators by Entanglement Forging

Andrew Eddins,Sarah Sheldon,Antonio Mezzacapo,Mario Motta,Charles Hadfield,Tanvi P Gujarati,Sergey Bravyi

doi:10.1103/prxquantum.3.010309

Abstract

Quantum computers are promising for simulations of chemical and physical systems, but the limited capabilities of today's quantum processors permit only small, and often approximate, simulations. Here we present a method, classical entanglement forging, that harnesses classical resources to capture quantum correlations and double the size of the system that can be simulated on quantum hardware. Shifting some of the computation to classical post-processing allows us to represent ten spin-orbitals on five qubits of an IBM Quantum processor to compute the ground state energy of the water molecule in the most accurate simulation to date. We discuss conditions for applicability of classical entanglement forging and present a roadmap for scaling to larger problems.

Highlights

Simulating quantum systems is an especially hard task for classical computers, making the realization of quantum computers potentially revolutionary for the study of chemistry, materials science, and fundamental physics
We theoretically describe the scheme, demonstrate it with a variational quantum eigensolver [23] (VQE) simulation in which five qubits capture the behavior of ten spin orbitals of the water molecule [24]
Theoretical description of classically forged entanglement begins with Schmidt decomposition [Fig. 1(a)], a standard application of singular value decomposition (SVD) that allows one to write any state |ψ of a bipartite N + N qubit system as

Summary

Introduction

Simulating quantum systems is an especially hard task for classical computers, making the realization of quantum computers potentially revolutionary for the study of chemistry, materials science, and fundamental physics. We repeat all experiments on a noiseless classical simulator, first verifying that this trend persists in the absence of gate errors (orange circles), and second observing that accuracy in the stretched regime improves substantially upon increasing the number of represented bit-string states k from three to six (purple squares), enabling the forging to describe stronger entanglement at the expense of sampling more distinct circuits.

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Results

Conclusion