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Published February 9, 2023 | Submitted
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Efficient Mean-Field Simulation of Quantum Circuits Inspired by the Many-Electron Problem

Abstract

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.

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 https://quest.qtechtheory.org. The QC drawings were preparedusing the Quantikz LaTeX package, which can be downloaded at https://ctan.org/pkg/quantikz. The QC-DFT Python code will be made available in the CaltechDATA repository. The authors declare no competing interests.

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Additional details

Created:
August 20, 2023
Modified:
October 24, 2023