Abstract
To realize quantum Boolean circuits, Toffoli gates are often used as logic primitives. Then Toffoli gates are decomposed to physically realizable gates, i.e., CNOT, H and T gates when we consider fault-tolerant implementation. The realization cost of a T gate is huge compared to the other gates, and thus we often consider the number of T gates. We need seven T gates to decompose a Toffoli gate. However, if we allow to add some relative phases to some output quantum states, we can implement a Toffoli gate by only four T gates. Such an approximate Toffoli gate is called a relative-phase Toffoli gate (RTOF). This paper proposes an optimization method of quantum circuit by using RTOFs. When we optimize a circuit by replacing a Toffoli gate with a RTOF, some relative phase errors are added. Our method tries to correct such relative phases by using S gates.
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Kuroda, S., Yamashita, S. (2022). Optimization of Quantum Boolean Circuits by Relative-Phase Toffoli Gates. In: Mezzina, C.A., Podlaski, K. (eds) Reversible Computation. RC 2022. Lecture Notes in Computer Science, vol 13354. Springer, Cham. https://doi.org/10.1007/978-3-031-09005-9_2
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DOI: https://doi.org/10.1007/978-3-031-09005-9_2
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