Minimal universal two-qubit controlled-NOT-based circuits (8 pages)

Ville Bergholm, Juha J. Vartiainen

Stephen S. Bullock, Vivek Shende

Colin P. Williams, Farrokh Vatan

Guifré Vidal, Christopher M. Dawson

We consider quantum circuits made of controlled-NOT (CNOT) gates and single-qubit unitary gates and look for constructions that minimize the use of CNOT gates. We show, by means of an explicit quantum circuit, that three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates and provide a simple characterization for them.

Dagmar Bruß, ARTUR K. EKERT, Susana F. Huelga +2 more

Mark W. Coffey, Ron Deiotte, Torey Semi

Recent papers in Physical Review A have considered small quantum circuit decompositions in terms of a minimal number of controlled-NOT (CNOT) gates. Specifically, we point out errors in the papers by Vidal and Dawson [Phys. Rev. A 69, 010301(R) (2004)] and by Shende et al. [Phys. Rev. A 70, 012310 (2004)].