Quantum accelerated approach to the thermal state of classical all-to-all connected spin systems with applications to pattern retrieval in the Hopfield neural network

Fiorelli, Eliana; Rotondo, Pietro; Marcuzzi, Matteo; Garrahan, Juan P.; Lesanovsky, Igor

Abstract

We explore the question as to whether quantum effects can yield a speedup of the nonequilibrium evolution of fully connected quadratic spin models towards a classical thermal state. In our approach we exploit the fact that the thermal state of a spin system can be mapped onto a node-free quantum state whose coefficients are given by thermal weights. This perspective permits the construction of a dissipative yet quantum dynamics which encodes in its stationary state the thermal state of the original problem. We show for the case of an all-to-all connected Ising spin model that an appropriate transformation of this dissipative dynamics allows us to interpolate between a regime in which the order parameter obeys the classical equations of motion under Glauber dynamics and a quantum regime with an accelerated transient timescale before approaching stationarity. We show that this effect enables, in principle, a speedup of pattern retrieval in a Hopfield neural network.

Citation

Fiorelli, E., Rotondo, P., Marcuzzi, M., Garrahan, J. P., & Lesanovsky, I. (2019). Quantum accelerated approach to the thermal state of classical all-to-all connected spin systems with applications to pattern retrieval in the Hopfield neural network. Physical Review A, 99(3), Article 032126. https://doi.org/10.1103/physreva.99.032126

• Journal Article Type: Article
• Acceptance Date: Mar 11, 2019
• Online Publication Date: Mar 29, 2019
• Publication Date: Mar 29, 2019
• Deposit Date: Apr 30, 2019
• Publicly Available Date: Apr 30, 2019
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 99
• Issue: 3
• Article Number: 032126
• DOI: https://doi.org/10.1103/physreva.99.032126
• Public URL: https://nottingham-repository.worktribe.com/output/1873704
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.032126
• Additional Information: Quantum accelerated approach to the thermal state of classical all-to-all connected spin systems with applications to pattern retrieval in the Hopfield neural network, Eliana Fiorelli, Pietro Rotondo, Matteo Marcuzzi, Juan P. Garrahan, and Igor Lesanovsky, Phys. Rev. A 99, 032126.