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Permutation-invariant quantum circuits
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abstract
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into quantum circuits. The permutation symmetry is the supergroup of all other discrete groups. We identify the permutation with a $\operatorname{SWAP}$ operation on the qubits. Based on the extension of the symmetry into the corresponding Lie algebra, quantum circuit element construction is shown via exponentiation. This allows for ready integration of the permutation group symmetry into quantum circuit ansatzes. The scaling of the number of parameters is found to be $\mathcal{O}(n^3)$, significantly lower than the general case and an indication that symmetry restricts the applicability of quantum computing. We also show how to adapt existing circuits to be invariant under a permutation symmetry by modification.
Forward citations
Cited by 4 Pith papers
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Enabling Lie-Algebraic Classical Simulation beyond Free Fermions
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Clique detection using symmetry-restricted quantum circuits
Permutation-invariant quantum circuits label cliques in small random graphs more accurately than cyclic-invariant or standard ansatze in simulation.
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Symmetric quantum states: a review of recent progress
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