Quantum state transfer on 2D lattices: A low-energy effective Hamiltonian approach

Abstract

We investigate the transfer of arbitrary single qubit states through a rectangular 2D lattice hosting the isotropic Heisenberg model under a magnetic field along the z direction, where the spin-spin interaction strengths along the vertical sublattices, referred to as rungs, are much stronger than the interactions along other sublattices. Using the rung-rung interaction as perturbation, the model can be mapped to an effective 1D model, and the transfer of low-energy rung states from one rung to another can be represented by a transfer of an arbitrary single-qubit state from one lattice site to another on the 1D effective lattice defined by the effective 1D Hamiltonian. Exploiting this, we propose protocols for transferring arbitrary single-qubit states from one lattice site to another by using specific encoding (decoding) of the single-qubit state into (from) the rung states. We demonstrate that this protocol leads to a quantum advantage in the single-qubit state transfer.