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

This paper addresses the question of how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction . We present a general method which is based on the K 1 AK 2 decomposition of unitary matrices ∊ SU (4) to calculate the smallest number of two-qubit gates U int ( t ) (based on ) 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.