Exact canonical decomposition of two-qubit operators in terms of CNOT

Authors:
Mark W. Coffey;Ron Deiotte
Affiliations:
Department of Physics, Colorado School of Mines, Golden, USA 80401;Department of Physics, Colorado School of Mines, Golden, USA 80401
Venue:
Quantum Information Processing
Year:
2010

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Quantum computation and quantum information

Quantum computation and quantum information
Nonlocal Properties of Two-Qubit Gates and Mixed States, and the Optimization of Quantum Computations

Quantum Information Processing

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Abstract

The canonical decomposition for two-qubit operators has proven very useful for applications in quantum computing. This decomposition generates equivalence classes up to local quantum gates. We provide a variety of complete, explicit decompositions of given two-qubit operators in terms of single, double, and triple controlled-NOT (CNOT) gates. By analytically addressing the needed pre- and post-tensor product factors, we demonstrate that exact results are possible, even when a parameter is included. The examples given are of interest to superconducting qubit, spin-based, dipolar molecule, and other quantum information processing systems.