Polylogarithmic-depth controlled-NOT gates without ancilla qubits

Baptiste Claudon (), Julien Zylberman, César Feniou, Fabrice Debbasch, Alberto Peruzzo and Jean-Philip Piquemal ()
Additional contact information
Baptiste Claudon: Advanced Research Department
Julien Zylberman: LERMA
César Feniou: Advanced Research Department
Fabrice Debbasch: LERMA
Alberto Peruzzo: Advanced Research Department
Jean-Philip Piquemal: Advanced Research Department

Nature Communications, 2024, vol. 15, issue 1, 1-8

Abstract: 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 introduces Cn(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 $$\Theta (\log {(n)}^{3})$$ Θ ( log ( n ) 3 ) , an approximating one without ancilla qubits with a circuit depth $${{{{{{{\mathcal{O}}}}}}}}(\log {(n)}^{3}\log (1/\epsilon ))$$ O ( log ( n ) 3 log ( 1 / ϵ ) ) and an exact one with an adjustable-depth circuit which decreases with the number m≤n of ancilla qubits available as $${{{{{{{\mathcal{O}}}}}}}}(\log {(n/\lfloor m/2\rfloor )}^{3}+\log (\lfloor m/2\rfloor ))$$ O ( log ( n / ⌊ m / 2 ⌋ ) 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.

Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/s41467-024-50065-x Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-50065-x

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-024-50065-x

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().