An analytical decomposition protocol for optimal implementation of two-qubit entangling gates
M. Blaauboer, R. L. de Visser
Abstract
This paper addresses the question how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction Hint. We present a general method which is based on the K1 A K2 decomposition of unitary matrices in SU(4) to calculate analytically the smallest number of two-qubit gates Uint [based on Hint] and single-qubit rotations, and the explicit sequence of these operations that are required to implement U. We illustrate our protocol by calculating the implementation of (1) the transformation from standard basis to Bell basis, (2) the CNOT gate, and (3) the quantum Fourier transform for two kinds of interaction - Heisenberg exchange interaction and quantum inductive coupling - and discuss the relevance of our results for solid-state qubits.
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