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quant-ph2003★ 11 cited
The simplified Toffoli gate implementation by Margolus is optimal
Guang Song, Andreas Klappenecker
Unitary operations are expressed in the quantum circuit model as a finite sequence of elementary gates, such as controlled-not gates and single qubit gates. We prove that the simpl…
math.CO2003★ 17 cited
Discrete Green's functions for products of regular graphs
Robert B. Ellis
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems…
math.FA2003★ 2 cited
Geometric Aspects of Frame Representations of Abelian Groups
Akram Aldroubi, David Larson, Wai-Shing Tang +1
We consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by c…