Towards a variational Jordan–Lee–Preskill quantum algorithm

Journal article

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 λ ϕ 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 Lehmann—Symanzik—Zimmermann 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.

Authors: Liu, J; Li, Z; Zheng, H; Yuan, X; Sun, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Machine Learning: Science and Technology
• Volume: 3
• Issue: 4
• Pages: 045030-045030
• Publication date: 2022-11-04
• DOI: 10.1088/2632-2153/aca06b
• EISSN: 2632-2153
• ISSN: 2632-2153
• Language: English
• Keywords: Quantum phase estimation algorithm; Quantum state; Mathematics; Ansatz; Open quantum system; Quantum algorithm; Quantum computer; Quantum mechanics; Algorithm; Qubit; Physics; Quantum network; Quantum information; Computer science; Quantum; Quantum circuit