@article {15718,
	title = {Asymptotically Optimal Quantum Circuits for d-Level Systems},
	journal = {Physical Review LettersPhys. Rev. Lett.},
	volume = {94},
	year = {2005},
	month = {2005/06/14/},
	pages = {230502 - 230502},
	abstract = {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.},
	doi = {10.1103/PhysRevLett.94.230502},
	url = {http://link.aps.org/doi/10.1103/PhysRevLett.94.230502},
	author = {Bullock,Stephen S. and O{\textquoteright}Leary,Dianne P. and Brennen,Gavin K.}
}
