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Qubit-efficient simulation of thermal states with quantum tensor networks

Zhang, Yuxuan and Jahanbani, Shahin and Niu, Daoheng and Haghshenas, Reza and Potter, Andrew C. (2022) Qubit-efficient simulation of thermal states with quantum tensor networks. Physical Review B, 106 (16). Art. No. 165126. ISSN 2469-9950. doi:10.1103/physrevb.106.165126.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Zhang, Yuxuan0000-0001-5477-8924
Jahanbani, Shahin0000-0003-1924-9909
Niu, Daoheng0000-0003-1097-184X
Haghshenas, Reza0000-0002-5593-8915
Additional Information:We thank Tomotaka Kuwahara for helpful discussion, and Garnet Chan, Michael Foss-Feig, David Hayes, Shyam Shankar, and Mike Zaletel for insightful conversations and previous related collaborations. This work was supported by NSF Award DMR-2038032 and the Alfred P. Sloan Foundation through a Sloan Research Fellowship (ACP). This research was undertaken thanks, in part, to funding from the Max Planck-UBC-UTokyo Center for Quantum Materials and the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program.
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Max Planck-UBC-UTokyo Center for Quantum MaterialsUNSPECIFIED
Canada First Research Excellence FundUNSPECIFIED
Issue or Number:16
Record Number:CaltechAUTHORS:20221117-155430600.6
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117904
Deposited By: Research Services Depository
Deposited On:30 Nov 2022 18:58
Last Modified:30 Nov 2022 18:58

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