Gibbs state sampling via cluster expansions

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 $\rho_8$.Comment: 8 pages, 8 figures, and supplementary materia

High-fidelity dimer excitations using quantum hardware

Many-body entangled quantum spin systems exhibit emergent phenomena such as topological quantum spin liquids with distinct excitation spectra accessed in inelastic neutron scattering (INS) experiments. Here we simulate the dynamics of a quantum spin dimer, the basic quantum unit of emergent many-body spin systems. While canonical Trotterization methods require deep circuits precluding long time-scale simulations, we demonstrate 'direct' Resource-Efficient Fast-forwarding (REFF) measurements with short-depth circuits that can be used to capture longer time dynamics on quantum hardware. The temporal evolution of the 2-spin correlation coefficients enabled the calculation of the dynamical structure factor $S(\mathbf{Q},\omega)$ - the key component of the neutron scattering cross-section. We simulate the triplet gap and the triplet splitting of the quantum dimer with sufficient fidelity to compare to experimental neutron data. Our results on current circuit hardware pave an important avenue to benchmark, or even predict, the outputs of the costly INS experiments.Comment: 24 pages, 3 tables, 16 figures, main text and supplementary material