Quantum Optimization with Arbitrary Connectivity Using Rydberg Atom Arrays

Abstract

Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum-weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including maximum-weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.5 MoreReceived 14 September 2022Revised 14 December 2022Accepted 4 January 2023DOI:https://doi.org/10.1103/PRXQuantum.4.010316Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBoolean satisfiability problemNP-hard problemsQuantum information architectures & platformsQuantum softwarePhysical SystemsAtomsRydberg atoms & moleculesQuantum InformationAtomic, Molecular & OpticalStatistical Physics