Efficient classical algorithms for simulating symmetric quantum systems
- URL: http://arxiv.org/abs/2211.16998v4
- Date: Tue, 21 Nov 2023 19:11:41 GMT
- Title: Efficient classical algorithms for simulating symmetric quantum systems
- Authors: Eric R. Anschuetz and Andreas Bauer and Bobak T. Kiani and Seth Lloyd
- Abstract summary: We show that classical algorithms can efficiently emulate 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-invariantians specified in the symmetrized Pauli basis.
- Score: 4.416367445587541
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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