Physics – Quantum Physics
Scientific paper
2005-09-22
Quantum Information and Computation, Vol. 6, 436 (2006)
Physics
Quantum Physics
16 pages, 3 figures, 2 tables
Scientific paper
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 (PRL 94 230502) describes quantum circuits for qudits which require O(d^n) two-qudit gates for state synthesis and O(d^{2n}) 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.
Brennen Gavin K.
Bullock Stephen S.
O'Leary Dianne P.
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