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arXiv · 1311.1074

Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries

Adam Paetznick·Krysta M. Svore
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Abstract

We present a decomposition technique that uses non-deterministic circuits to approximate an arbitrary single-qubit unitary to within distance $\epsilon$ and requires significantly fewer non-Clifford gates than existing techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rotation to within distance $\epsilon$, where the number of $T$ gates scales as $1.26\log_2(1/\epsilon) - 3.53$, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of $2.4\log_2(1/\epsilon) - 3.28$ can be achieved for arbitrary unitaries and a small range of $\epsilon$, which is roughly twice as good as optimal deterministic decomposition methods.

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Adam Paetznick, Krysta M. Svore. 2013-11-05. Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries. https://arxiv.org/abs/1311.1074

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