Qubit-efficient simulation of thermal states with quantum tensor networks

• URL: http://arxiv.org/abs/2205.06299v2
• Date: Thu, 13 Oct 2022 22:42:56 GMT
• Title: Qubit-efficient simulation of thermal states with quantum tensor networks
• Authors: Yuxuan Zhang, Shahin Jahanbani, Daoheng Niu, Reza Haghshenas, and Andrew C. Potter
• Abstract summary: We present a holographic quantum simulation algorithm to variationally prepare thermal states of interacting quantum manybody systems. We demonstrate a small-scale proof of principle demonstration of this technique on Quantinuum's trapped-ion quantum processor.
• Score: 13.128146097939263
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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