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Holographic simulation of correlated electrons on a trapped ion quantum processor

Niu, Daoheng and Haghshenas, Reza and Zhang, Yuxuan and Foss-Feig, Michael and Chan, Garnet Kin-Lic and Potter, Andrew C. (2021) Holographic simulation of correlated electrons on a trapped ion quantum processor. . (Unpublished)

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We develop holographic quantum simulation techniques to prepare correlated electronic ground states in quantum matrix product state (qMPS) form, using far fewer qubits than the number of orbitals represented. Our approach starts with a holographic technique to prepare a compressed approximation to electronic mean-field ground-states, known as fermionic Gaussian matrix product states (GMPS), with a polynomial reduction in qubit- and (in select cases gate-) resources compared to existing techniques. Correlations are then introduced by augmenting the GMPS circuits in a variational technique which we denote GMPS+U. We demonstrate this approach on Quantinuum's System Model H1 trapped-ion quantum processor for 1d models of correlated metal and Mott insulating states. Focusing on the 1d Fermi-Hubbard chain as a benchmark, we show that GMPS+U methods faithfully capture the physics of correlated electron states, including Mott insulators and correlated Luttinger liquid metals, using considerably fewer parameters than problem-agnostic variational circuits.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Haghshenas, Reza0000-0002-5593-8915
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:Attribution-ShareAlike 4.0 International (CC BY-SA 4.0). We thank Itamar Kimchi, Roger Mong, and Michael Zaletel for insightful conversations. We acknowledge support from NSF award DMR-2038032 (YZ, AP), NSF-Converence Accelerator Track C award DMR- (DN, GKC), from the Alfred P. Sloan Foundation through a Sloan Research Fellowship (AP). RH was supported by the US Department of Energy, Office of Science, via Award No. DE-SC0019374. Additional support from GKC was provide by the Simons Collaboration on the Many-electron Problem and the Simons Investigatorship. 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. Numerical calculations were performed using supercomputing resources at the Texas Advanced Computing Center (TACC).
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0019374
Simons FoundationUNSPECIFIED
Max Planck-UBC-UTokyo Center for Quantum MaterialsUNSPECIFIED
Canada First Research Excellence FundUNSPECIFIED
Record Number:CaltechAUTHORS:20220124-192941188
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113075
Deposited By: George Porter
Deposited On:24 Jan 2022 20:19
Last Modified:24 Jan 2022 20:19

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