Time evolution of uniform sequential circuits

Astrakhantsev, Nikita; Lin, Sheng-Hsuan; Pollmann, Frank; Smith, Adam

Abstract

Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational Ansatz to represent infinite translation-invariant quantum states. We show numerically that this Ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favorable scaling of the Ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.

Citation

Astrakhantsev, N., Lin, S.-H., Pollmann, F., & Smith, A. (2023). Time evolution of uniform sequential circuits. Physical Review Research, 5(3), Article 033187. https://doi.org/10.1103/physrevresearch.5.033187

• Journal Article Type: Article
• Acceptance Date: Aug 21, 2023
• Online Publication Date: Sep 14, 2023
• Publication Date: 2023-09
• Deposit Date: Oct 5, 2023
• Publicly Available Date: Oct 6, 2023
• Journal: Physical Review Research
• Electronic ISSN: 2643-1564
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Issue: 3
• Article Number: 033187
• DOI: https://doi.org/10.1103/physrevresearch.5.033187
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/25394537
• Publisher URL: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.033187