A new cultivation protocol prepares reusable logical catalysts as eigenstates of high-period Clifford circuits to implement exact Z^{2^{-b}} phase gates with constant online depth in surface codes.
Efficient synthesis of universal Repeat-Until-Success circuits
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abstract
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.
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Search-based approximate diagonalization followed by analytical inversion yields high-precision multi-qubit Clifford+T circuits with 95% fewer non-Clifford gates on real-algorithm benchmarks.
Pinnacle Architecture using QLDPC codes reduces physical qubits needed to factor RSA-2048 to under 100,000 at 10^{-3} error rate.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
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.
citing papers explorer
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Cultivating logical catalysts for fault-tolerant dyadic phase rotations
A new cultivation protocol prepares reusable logical catalysts as eigenstates of high-period Clifford circuits to implement exact Z^{2^{-b}} phase gates with constant online depth in surface codes.
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High-Precision Multi-Qubit Clifford+T Synthesis by Unitary Diagonalization
Search-based approximate diagonalization followed by analytical inversion yields high-precision multi-qubit Clifford+T circuits with 95% fewer non-Clifford gates on real-algorithm benchmarks.
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The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes
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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Magic state cultivation: growing T states as cheap as CNOT gates
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
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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.