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arXiv · 2303.12979

Optimal Synthesis of Multi-Controlled Qudit Gates

Wei Zi·Qian Li·Xiaoming Sun
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Abstract

We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum algorithms implemented on qudits. In particular, we obtain (i) a linear-size and one-clean-ancilla synthesis of multi-controlled qudit gates; (ii) an optimal-size and one-clean-ancilla synthesis of unitaries on qudits; (iii) a near-optimal-size and ancilla-free/one-borrowed-ancilla implementation of classical reversible functions as qudit gates.

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Wei Zi, Qian Li, Xiaoming Sun. 2023-03-23. Optimal Synthesis of Multi-Controlled Qudit Gates. https://arxiv.org/abs/2303.12979

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