Exponentially improved quantum simulation of scalar QFT

TL;DR

This paper introduces an exponential improvement in quantum simulation of scalar QFT by reducing circuit depth and Trotter errors through a novel diagonalization approach, enabling more efficient near-term quantum computations.

Contribution

The authors present a new digitization method that significantly reduces circuit depth and errors in scalar QFT simulations, outperforming previous amplitude-basis approaches.

Findings

Exponential reduction in circuit depth and CNOT gates for scalar QFT simulation.

Faster convergence of occupation-basis digitization compared to amplitude-basis.

Benchmarking with Lorentzian energy-energy correlator shows improved efficiency.

Abstract

Quantum simulations of scalar quantum field theories (QFT) provide important benchmarks for demonstrating quantum advantage. We revisit digitization in the occupation basis, which is typically hindered by unfavorable circuit depth scaling. We present an approach that achieves exponential reductions in circuit depth and significantly mitigates Trotter errors by diagonalizing field operators prior to their decomposition into Pauli strings. Focusing on a scalar QFT in 2+1 dimensions, we show that this method substantially reduces circuit depth and CNOT gate counts for time evolution. Using the Lorentzian energy-energy correlator as a benchmark observable, we find parameter regimes in which occupation-basis digitization converges more rapidly with respect to local truncation than the amplitude-basis approach of Jordan, Lee, and Preskill. These results provide both algorithmic advances and phenomenological benchmarks for studies of light-ray observables on near-term quantum devices.