TY - JOUR
T1 - Asymptotically optimal quantum circuits for d-level systems
AU - Bullock, Stephen S.
AU - O'Leary, Dianne P.
AU - Brennen, Gavin K.
PY - 2005/6/17
Y1 - 2005/6/17
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=27144464549&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.94.230502
DO - 10.1103/PhysRevLett.94.230502
M3 - Article
C2 - 16090450
AN - SCOPUS:27144464549
SN - 0031-9007
VL - 94
SP - 1
EP - 4
JO - Physical Review Letters
JF - Physical Review Letters
IS - 23
M1 - 230502
ER -