Preparation of an arbitrary two-qubit quantum gate on two spins with an anisotropic Heisenberg interaction

TL;DR

This paper presents a two-step method for implementing arbitrary two-qubit quantum gates using anisotropic Heisenberg interactions, involving system evolution and targeted magnetic pulses, with potential application to ultracold atoms.

Contribution

It develops specific conditions for realizing various quantum gates on two spins with anisotropic Heisenberg interaction, including practical implementation considerations.

Findings

Conditions for SWAP, iSWAP, and entangled gates are derived.

Method applicable to ultracold atoms in optical lattices.

Two-step process effectively creates desired quantum gates.

Abstract

We consider the two-step method [A. R. Kuzmak and V. M. Tkachuk, Phys. Lett. A 378 (2014) 1469] for preparation of an arbitrary quantum gate on two spins with anisotropic Heisenberg interaction. At the first step, the system evolves during some period of time. At the second step, we apply pulsed magnetic field individually to each spin. We obtain the conditions for realization of SWAP, iSWAP, $\sqrt{SWAP}$ and entangled gates. Finally, we consider the implementation of this method on the physical system of ultracold atoms in optical lattice.