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Svore, “RepeatUntilSuccess: Nondeterministic decomposition of singlequbit unitaries,” p
, 2013
"... We present a decomposition technique that uses nondeterministic circuits to approximate an arbitrary singlequbit unitary to within distance and requires significantly fewer nonClifford gates than existing techniques. We develop “RepeatUntilSuccess ” (RUS) circuits and characterize unitaries th ..."
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We present a decomposition technique that uses nondeterministic circuits to approximate an arbitrary singlequbit unitary to within distance and requires significantly fewer nonClifford gates than existing techniques. We develop “RepeatUntilSuccess ” (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 nonClifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary singlequbit Zaxis rotation to within distance , where the number of T gates scales as 1.26 log2(1/) − 3.53, an improvement of roughly threefold over stateoftheart techniques. We then extend our algorithm and show that a scaling of 2.4 log2(1/) − 3.28 can be achieved for arbitrary unitaries and a small range of , which is roughly twice as good as optimal deterministic decomposition methods. 1
Quantum Circuit Optimization by Hadamard Gate Reduction
"... Abstract. Due to its faulttolerant gates, the Clifford+T library consisting of Hadamard (denoted by H), T, and CNOT gates has attracted interest in the synthesis of quantum circuits. Since the implementation of T gates is expensive, recent research is aiming at minimizing the use of such gates. It ..."
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Abstract. Due to its faulttolerant gates, the Clifford+T library consisting of Hadamard (denoted by H), T, and CNOT gates has attracted interest in the synthesis of quantum circuits. Since the implementation of T gates is expensive, recent research is aiming at minimizing the use of such gates. It has been shown that Tdepth optimizations can be implemented efficiently for circuits consisting only of T and CNOT gates and that H gates impede the optimization significantly. In this paper, we investigate the role of H gates in reducing the Tcount and Tdepth for quantum circuits. To reduce the number of H gates, we propose several algorithms targeting different steps in the synthesis of reversible functions as quantum circuits. Experiments show the effect of H gate reductions on the costs for Tcount and Tdepth. Our approach yields a significant improvement of up to 88 % in the final Tdepth compared to the best known Tdepth optimization technique. 1
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"... Resource optimization for faulttolerant quantum computing by ..."
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