Optimal realizations of controlled unitary gates Academic Article

abstract

• The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions trU
  eq 0, tr(UX)
  eq 0, and detU
  eq 1. We also derive optimal implementations in the remaining non-generic cases. realizations of controlled unitary gates (pp139-155) G. Song and A. Klappenecker The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions trU
  eq 0, tr(UX)
  eq 0, and detU
  eq 1. We also derive optimal implementations in the remaining non-generic cases.

authors

• Klappenecker, Andreas

published proceedings

• QUANTUM INFORMATION & COMPUTATION

author list (cited authors)

• Song, G., & Klappenecker, A.

citation count

• 6

complete list of authors

• Song, G||Klappenecker, A

publication date

• March 2003

publisher

• Rinton Press  Publisher

published in

• Quantum Information and Computation  Journal

keywords

• Controlled Unitary Gates
• Lower Bounds
• Quantum Circuits
• Quantum Gates

Digital Object Identifier (DOI)

• 10.26421/qic3.2-5

start page

• 139

end page

• 156

volume

• 3

issue

• 2

URL

• http://dx.doi.org/10.26421/qic3.2-5