Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density Functional Theory

TL;DR

This paper introduces a density functional theory-inspired mean-field method for simulating quantum circuits, achieving over 90% accuracy in predicting single-qubit probabilities with linear resource scaling.

Contribution

The authors develop a novel mean-field approach for quantum circuit simulation using DFT-inspired functionals, enabling efficient approximate predictions of qubit probabilities.

Findings

Predicts single-qubit probabilities with over 90% accuracy

Uses linear memory and computational resources in qubit number

Provides a new framework for approximate quantum circuit simulation

Abstract

Exact simulations of quantum circuits (QCs) are currently limited to $\sim$50 qubits because the memory and computational cost required to store the QC wave function scale exponentially with qubit number. Therefore, developing efficient schemes for approximate QC simulations is a current research focus. Here we show simulations of QCs with a method inspired by density functional theory (DFT), a widely used approach to study many-electron systems. Our calculations can predict marginal single-qubit probabilities (SQPs) with over 90% accuracy in several classes of QCs with universal gate sets, using memory and computational resources linear in qubit number despite the formal exponential cost of the SQPs. This is achieved by developing a mean-field description of QCs and formulating optimal single- and two-qubit gate functionals $-$ analogs of exchange-correlation functionals in DFT $-$ to evolve the SQPs without computing the QC wave function. Current limitations and future extensions of this formalism are discussed.