Efficient classical algorithms for simulating symmetric quantum systems
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q-2023-11-28-1189.pdf
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1.16 MB
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Checksum (MD5)
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Author(s)
Anschuetz, Eric R.
Bauer, Andreas
Kiani, Bobak T.
Lloyd, Seth
Date Issued
November 28, 2023
Journal
Quantum
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Citation
Efficient classical algorithms for simulating symmetric quantum systems, Anschuetz, Eric R. and Bauer, Andreas and Kiani, Bobak T. and Lloyd, Seth,Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, 7, 1189, 2023.
Version
Final published version
Abstract
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements.
Subjects
Physics and Astronomy (miscellaneous)
Atomic and Molecular Physics, and Optics
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.22331/q-2023-11-28-1189
