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Polylogarithmic-depth controlled-NOT gates without ancilla qubits
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DOI：10.1038/s41467-024-50065-x.png)
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Abstract
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Controlled operations are fundamental building blocks of quantum algorithms. Decomposing n-control-NOT gates (Cn(X)) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces Cn(X) circuits outperforming previous methods in the asymptotic and nonasymptotic regimes. Three distinct decompositions are presented: an exact one using one borrowed ancilla with a circuit depth Tolog onTHORN 3 THORN, an approximating one without ancilla qubits with a circuit depth Oolog onTHORN3 logo1=.THORNTHORN and an exact onewith an adjustable-depth circuit which decreaseswith the number m=n of ancilla qubits available as Oolog on=bm=2cTHORN3 + logobm=2cTHORNTHORN. The resulting exponential speedup is likely to have a substantial impact on fault-tolerant quantum computing by improving the complexities of countless quantum algorithms with applications ranging from quantum chemistry to physics, finance and quantum machine learning.
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