Towards a variational Jordan-Lee-Preskill quantum algorithm

TL;DR

This paper develops a variational quantum algorithm for simulating 1+1 dimensional quantum field theory, focusing on encoding, state preparation, and time evolution, with numerical results demonstrating its potential for near-term quantum devices.

Contribution

It introduces a variational quantum simulation framework for quantum field theory, including novel encoding methods and strategies to improve efficiency and address spectral crowding.

Findings

Numerical simulations validate the algorithm's effectiveness.

Encoding with harmonic oscillator basis improves computational efficiency.

Strategies to mitigate spectral crowding enhance simulation accuracy.

Abstract

Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1+1 dimensional $\lambda \phi^4$ quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the LSZ reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the "spectral crowding" problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.