Recognizing Small Circuit Structure in Two-Qubit Operators
V V. Shende, Stephen Bullock, I L. Markov
This work describes numerical tests which determine whether a two-qubit quantum computation has an atypically simple quantum circuit. Specifically, we describe forumulae, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-not gates with all other gates being local unitary. Circuit diagrams are provided in each case. We expect significant impact in physical implementations where controlled-not's are more difficult than one-qubit computations.Our results can be contrasted with those by Zhang et al., Bullock and Markov, Vidal and Dawson, and Shende et al. In these works, small quantum circuits are achieved for arbitrary two-qubit operators, and the latter two prove three controlled-not's suffice. However, unitary operators with the sort of structure described above may not be detected. Our work provides results similar to those by Song and Klappenecker but for a wider range of operators.
, Bullock, S.
and Markov, I.
Recognizing Small Circuit Structure in Two-Qubit Operators, Physical Review Letters, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50705
(Accessed February 25, 2024)