Building spatial symmetries into parameterized quantum circuits for faster training

Journal Article · 03 January 2024 · Quantum Science and Technology

DOI: https://doi.org/10.1088/2058-9565/ad152e · OSTI ID:2278748

Sauvage, Frédéric ; Larocca, Martín; Coles, Patrick J. ; Cerezo, M.

Abstract Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturally emerges when carefully considering spatial symmetries (i.e. the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuitstructure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2278748
• Report Number(s): LA-UR--22-27391
• Journal Information: Quantum Science and Technology, Journal Name: Quantum Science and Technology Journal Issue: 1 Vol. 9; ISSN 2058-9565
• Publisher: IOP PublishingCopyright Statement
• Country of Publication: United Kingdom
• Language: English