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Heuristic and Optimal Synthesis of CNOT and Clifford Circuits
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Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In this work we present methods for CNOT and general Clifford circuit synthesis which can be used to minimise either the entangling two-qubit gate count or the circuit depth. We present three families of algorithms - optimal synthesis which works on small circuits, A* synthesis for intermediate-size circuits and greedy synthesis for large circuits. We benchmark against existing methods in the literature and show that our approach results in circuits with lower two-qubit gate count than previous methods. The algorithms have been implemented in a GitHub repository for use by the classical and quantum computing community.
Forward citations
Cited by 3 Pith papers
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Lower bounds for the CNOT-complexity of linear reversible operators
An explicit family of linear reversible circuits is shown to require at least 4n−o(n) CNOT gates, asymptotically surpassing the cyclic permutations and yielding an n=17167 instance with complexity >3(n−1).
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Fast logical operations in quantum LDPC codes using simple resource states
A scheduler-code protocol jointly measures up to 20 commuting logical operators in quantum LDPC codes with ~1.7 cat states per operator, yielding up to 3x faster logical measurements and up to 74x faster Clifford circ...
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Noise-Aware Synthesis of Quantum LDPC Encoder Circuits via Two-Sided Hamming Descent
Two-sided Hamming descent plus noise-aware routing and live-range scheduling cuts CSS LDPC encoder CNOT counts by 53.8% aggregate and improves preparation fidelity under circuit-level noise.
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