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- W3208831820 abstract "The reversible implementation of classical functions accounts for the bulk of most known quantum algorithms. As a result, a number of reversible circuit constructions over the Clifford+$T$ gate set have been developed in recent years which use both the state and phase spaces, or $X$ and $Z$ bases, to reduce circuit costs beyond what is possible at the strictly classical level. We study and generalize two particular classes of these constructions: relative phase circuits, including Giles and Selinger's multiply-controlled $iX$ gates and Maslov's $4$ qubit Toffoli gate, and measurement-assisted circuits, including Jones' Toffoli gate and Gidney's temporary logical-AND. In doing so, we introduce general methods for implementing classical functions up to phase and for measurement-assisted termination of temporary values. We then apply these techniques to find novel $T$-count efficient constructions of some classical functions in space-constrained regimes, notably multiply-controlled Toffoli gates and temporary products." @default.
- W3208831820 created "2021-11-08" @default.
- W3208831820 creator A5004989555 @default.
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- W3208831820 date "2021-11-04" @default.
- W3208831820 modified "2023-10-17" @default.
- W3208831820 title "Phase-state duality in reversible circuit design" @default.
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- W3208831820 doi "https://doi.org/10.1103/physreva.104.052602" @default.
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