Asymptotically Optimal Quantum Circuits for d-Level Systems

Journal Article · Fri Jun 17 00:00:00 EDT 2005 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.94.230502· OSTI ID:20696368

Bullock, Stephen S ^[1]; O'Leary, Dianne P ^[1]; Brennen, Gavin K ^[2]

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1. Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8910 (United States)
2. Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420 (United States)

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 {theta}(d{sup 2n}) 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.

• OSTI ID: 20696368
• Journal Information: Physical Review Letters, Vol. 94, Issue 23; Other Information: DOI: 10.1103/PhysRevLett.94.230502; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
ASYMPTOTIC SOLUTIONS
INFORMATION THEORY
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS