An analytical decomposition protocol for optimal implementation of two-qubit entangling gates

Abstract

This paper addresses the question of how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction H int(t). We present a general method which is based on the K 1AK2 decomposition of unitary matrices ∈ SU(4) to calculate the smallest number of two-qubit gates Uint(t) (based on Hint(t)) 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. © 2008 IOP Publishing Ltd.