Gibbs state sampling via cluster expansions

• URL: http://arxiv.org/abs/2310.20129v1
• Date: Tue, 31 Oct 2023 02:36:24 GMT
• Title: Gibbs state sampling via cluster expansions
• Authors: Norhan M. Eassa, Mahmoud M. Moustafa, Arnab Banerjee, Jeffrey Cohn
• Abstract summary: Gibbs states can be used for several applications such as quantum simulation, machine learning, quantum optimization, and the study of open quantum systems. We propose a method based on sampling from a quasi-distribution consisting of tensor products of mixed states on local clusters. We present results for 4-spin linear chains with XY spin interactions, for which we obtain the $ZZ$ dynamical spin-spin correlation functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gibbs states (i.e., thermal states) can be used for several applications such as quantum simulation, quantum machine learning, quantum optimization, and the study of open quantum systems. Moreover, semi-definite programming, combinatorial optimization problems, and training quantum Boltzmann machines can all be addressed by sampling from well-prepared Gibbs states. With that, however, comes the fact that preparing and sampling from Gibbs states on a quantum computer are notoriously difficult tasks. Such tasks can require large overhead in resources and/or calibration even in the simplest of cases, as well as the fact that the implementation might be limited to only a specific set of systems. We propose a method based on sampling from a quasi-distribution consisting of tensor products of mixed states on local clusters, i.e., expanding the full Gibbs state into a sum of products of local "Gibbs-cumulant" type states easier to implement and sample from on quantum hardware. We begin with presenting results for 4-spin linear chains with XY spin interactions, for which we obtain the $ZZ$ dynamical spin-spin correlation functions. We also present the results of measuring the specific heat of the 8-spin chain Gibbs state $\rho_8$.

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