We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a $(d-1)$-dimensional cross section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix-product states (sto-qMPS). The parameters of the quantum circuits generating the qMPS and of the probability distribution generating the stochastic mixture are determined through a variational optimization procedure. We demonstrate a small-scale proof-of-principle demonstration of this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin chains over a wide temperature range using only a single pair of hardware qubits. Then, through classical simulations, we explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits and establish empirical relationships between the circuit resources and the accuracy of the variational free energy.

• Received 10 August 2022
• Revised 13 October 2022
• Accepted 17 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.165126