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Quantum Machine Learning Quantum Chemistry

Polylogarithmic-depth controlled-NOT gates without ancilla qubits

arXiv

Authors: Baptiste Claudon, Julien Zylberman, César Feniou, Fabrice Debbasch, Alberto Peruzzo, Jean-Philip Piquemal

Year

2023

Paper ID

53259

Status

Preprint

Abstract Read

~2 min

Abstract Words

144

Citations

N/A

Abstract

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

Why This Paper Matters

This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
It adds a 2023 reference point for readers tracking recent quantum research.
Controlled operations are fundamental building blocks of quantum algorithms.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2312.13206 [2] arXiv https://arxiv.org/abs/2312.13206 [3] Publisher https://arxiv.org/abs/2312.13206

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