Asymptotically optimal quantum circuits for d-level systems.

@article{Bullock2005AsymptoticallyOQ,
  title={Asymptotically optimal quantum circuits for d-level systems.},
  author={Stephen S. Bullock and Dianne P. O'Leary and G. K. Brennen},
  journal={Physical review letters},
  year={2005},
  volume={94 23},
  pages={
          230502
        }
}
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(2n)) gates… CONTINUE READING

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