Efficient circuits for exact-universal computation with qudits
(pp436-454)
Gavin K. Brennen, Stephen S. Bullock,
and Dianne P. O'Leary
doi:
https://doi.org/10.26421/QIC6.4-5-9
Abstracts:
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(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.
Key words:
Quantum circuits, gates, gate library |