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Efficient Mean-Field Simulation of Quantum Circuits Inspired by the Many-Electron Problem

Bernardi, Marco (2022) Efficient Mean-Field Simulation of Quantum Circuits Inspired by the Many-Electron Problem. . (Unpublished)

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Classical simulations can provide the exact wave function of quantum circuits (QCs), but are currently limited to ∼50 qubits due to their memory and computational cost, which scale exponentially with qubit number. As quantum hardware advances toward hundreds of interacting qubits, developing reliable schemes for approximate QC simulations has become a priority. Here we show efficient simulations of QCs with a method inspired by density functional theory (DFT), a widely used approach to study many-electron systems. We demonstrate accurate simulations of various QCs with universal gate sets, reaching up to a billion qubits in size, using only laptop calculations. Our simulations can predict marginal single-qubit probabilities (SQPs) with over 90\% accuracy, using memory and computational resources linear in qubit number despite the formal exponential cost of SQPs. We achieve these results by adopting a mean-field description of QCs, and formulating optimal single- and two-qubit gate functionals − analogs of exchange-correlation functionals in DFT − to evolve the SQPs without computing the QC wave function. Our findings pave the way for accurate simulations of large QCs and provide a blueprint to adapt electronic structure methods to QC simulations.

Item Type:Report or Paper (Discussion Paper)
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Bernardi, Marco0000-0001-7289-9666
Additional Information:Attribution 4.0 International (CC BY 4.0). This work was supported by the National Science Foundation under Grant No. 1750613, which provided for method development. M.B. was also supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Basic Energy Sciences, Scientific Discovery through Advanced Computing (SciDAC) program under Award Number DE-SC0022088, which supported code development. AUTHOR CONTRIBUTIONS. M.B. conceived and designed the research, performed the calculations and analysis, and wrote the manuscript. DATA AVAILABILITY. The data sets generated and analyzed in this study, as well as the QC-DFT codes, will be made available in the CaltechDATA repository. Additional data and information are available upon reasonable request. CODE AVAILABILITY. The QuEST code3 used for the exact QC simulations is an open source software, which can be downloaded at The QC drawings were preparedusing the Quantikz LaTeX package, which can be downloaded at The QC-DFT Python code will be made available in the CaltechDATA repository. The authors declare no competing interests.
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Department of Energy (DOE)DE-SC0022088
Record Number:CaltechAUTHORS:20230207-190610226
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119073
Deposited By: George Porter
Deposited On:09 Feb 2023 00:15
Last Modified:02 Jun 2023 01:29

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