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Efficient synthesis of universal Repeat-Until-Success circuits
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Recently, it was shown that Repeat-Until-Success (RUS) circuits can achieve a $2.5$ times reduction in expected $T$-count over ancilla-free techniques for single-qubit unitary decomposition. However, the previously best known algorithm to synthesize RUS circuits requires exponential classical runtime. In this paper we present an algorithm to synthesize an RUS circuit to approximate any given single-qubit unitary within precision $\varepsilon$ in probabilistically polynomial classical runtime. Our synthesis approach uses the Clifford+$T$ basis, plus one ancilla qubit and measurement. We provide numerical evidence that our RUS circuits have an expected $T$-count on average $2.5$ times lower than the theoretical lower bound of $3 \log_2 (1/\varepsilon)$ for ancilla-free single-qubit circuit decomposition.
Forward citations
Cited by 5 Pith papers
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Pinnacle Architecture using QLDPC codes reduces physical qubits needed to factor RSA-2048 to under 100,000 at 10^{-3} error rate.
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High-Precision Multi-Qubit Clifford+T Synthesis by Unitary Diagonalization
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Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation
Dyadic Phase Fixing reduces T-count by up to 70% versus gridsynth in quantum circuit compilation for fault-tolerant computing via numerical synthesis and automatic phase register sizing.
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