Efficient circuits for exact-universal computationwith qudits

Authors:
G. K. Brennen;S. S. Bullock;D. P. O'Leary
Affiliations:
Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland;Center for Computing Sciences, Institute for Defense Analyses, Bowie, MD;Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, Maryland and Mathematical and Computational Sciences Division, National Institute of Standards a ...
Venue:
Quantum Information & Computation
Year:
2006

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Abstract

This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate library containing arbitrary local unitaries and one two-qudit gate, CINC, is exact-universal. A recent paper [S.Bullock, D.O'Leary, and G.K. Brennen, Phys. Rev. Lett. 94, 230502 (2005)] describes quantum circuits for qudits which require O(dn) two-qudit gates for state synthesis and O(dn2) two-qudit gates for unitary synthesis, matching the respective lower bound complexities. In this work, we present the state-synthesis circuit in much greater detail and prove that it is correct. Also, the ⌈(n-2)/(d-2)⌉ ancillas required in the original algorithm may be removed without changing the asymptotics. Further, we present a new algorithm for unitary synthesis, inspired by the QR matrix decomposition, which is also asymptotically optimal.