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- W1915167278 abstract "Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize a RUS circuit to approximate any given single-qubit unitary to precision $ϵ$ over the $text{Clifford}+T$ basis. Surprisingly, the $T$ count of the synthesized RUS circuit surpasses the theoretical lower bound of $3text{ }{mathrm{log}}_{2}(1/ϵ)$ that holds for purely unitary single-qubit circuit decomposition. By taking advantage of measurement and an ancilla qubit, RUS circuits achieve an expected $T$ count of $1.15text{ }{mathrm{log}}_{2}(1/ϵ)$ for single-qubit $z$ rotations. Our method leverages the fact that the set of unitaries implementable by RUS protocols has a higher density in the space of all unitaries compared to the density of purely unitary implementations." @default.
- W1915167278 created "2016-06-24" @default.
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- W1915167278 date "2015-02-27" @default.
- W1915167278 modified "2023-10-15" @default.
- W1915167278 title "Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits" @default.
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- W1915167278 doi "https://doi.org/10.1103/physrevlett.114.080502" @default.
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