Asymptotically Optimal Quantum Circuits for d-Level Systems

TitleAsymptotically Optimal Quantum Circuits for d-Level Systems
Publication TypeJournal Articles
Year of Publication2005
AuthorsBullock SS, O’Leary DP, Brennen GK
JournalPhysical Review LettersPhys. Rev. Lett.
Pagination230502 - 230502
Date Published2005/06/14/

Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many d-level systems (qudits). Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of Θ(d2n) gates. This closes the complexity question for all d-level systems (d finite). The optimal asymptotic applies to systems with locality constraints, e.g., nearest neighbor interactions.