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Article Dans Une Revue Nature Communications Année : 2024

Polylogarithmic-depth controlled-NOT gates without ancilla qubits

Résumé

Controlled operations are fundamental building blocks of quantum algorithms. Decomposing $n$-control-NOT gates ($C^n(X)$) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces $C^n(X)$ circuits outperforming previous methods in the asymptotic and non-asymptotic regimes. Three distinct decompositions are presented: an exact one using one borrowed ancilla with a circuit depth $\Theta\left(\log(n)^{3}\right)$, an approximating one without ancilla qubits with a circuit depth $\mathcal O \left(\log(n)^{3}\log(1/\epsilon)\right)$ and an exact one with an adjustable-depth circuit which decreases with the number $m\leq n$ of ancilla qubits available as $O(log(2n/m)^3+log(m/2))$. 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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Dates et versions

hal-04357047 , version 1 (06-09-2024)

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B. Claudon, J. Zylberman, C. Feniou, F. Debbasch, A. Peruzzo, et al.. Polylogarithmic-depth controlled-NOT gates without ancilla qubits. Nature Communications, 2024, 15, pp.5886. ⟨10.1038/s41467-024-50065-x⟩. ⟨hal-04357047⟩
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