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• W1630276295 abstract "The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic oper-ations on quantum data, e.g., reversible arithmetic circuits. In physical implementations,however, TOFFOLI gates are decomposed into six CNOT gates and several one-qubit gates.Though this decomposition has been known for at least 10 years, we provide here thefirst demonstration of its CNOT-optimality. We study three-qubit circuits which containless than six CNOT gates and implement a block-diagonal operator, then show that theyimplicitly describe the cosine-sine decomposition of a related operator. Leveraging thecanonical nature of such decompositions to limit one-qubit gates appearing in respectivecircuits, we prove that the n-qubit analogue of the TOFFOLI requires at least 2n CNOTgates. Additionally, our results offer a complete classification of three-qubit diagonaloperators by their CNOT-cost, which holds even if ancilla qubits are available." @default.
• W1630276295 created "2016-06-24" @default.
• W1630276295 creator A5065370018 @default.
• W1630276295 creator A5077525113 @default.
• W1630276295 date "2009-05-01" @default.
• W1630276295 modified "2023-09-23" @default.
• W1630276295 title "On the CNOT-cost of TOFFOLI gates" @default.
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• W1630276295 doi "https://doi.org/10.5555/2011791.2011799" @default.
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