Optimising T-count is NP-hard

• URL: http://arxiv.org/abs/2310.05958v2
• Date: Tue, 17 Oct 2023 10:04:53 GMT
• Title: Optimising T-count is NP-hard
• Authors: John van de Wetering, Matt Amy
• Abstract summary: We find an upper bound to the T-count problem of $textNPtextNQP$ in a reversible classical circuit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this short note we show that Boolean satisfiability reduces to finding the optimal number of T gates of a quantum circuit, and hence that optimising T-count is NP-hard. We show that the same argument extends to optimising the number of Toffoli gates in a reversible classical circuit, and we furthermore find an upper bound to the T-count problem of $\text{NP}^{\text{NQP}}$.

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