Fast and efficient long-distance quantum state transfer in long-range spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> models

Abstract Quantum state transfer (QST) is investigated beyond the nearest-neighbour coupling scheme in long spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> linear chains. Exploiting the properties of the next-nearest neighbour Hamiltonian’s dispersion relation, it is shown that with minimal engineering, i.e. an on-site magnetic field on the two end sites and only a few symmetrically-modified end inter-site couplings, an average transfer fidelity above 99% can be achieved. To leading order, the required time scales linearly with the length of the chain. Such a fast, high-quality QST is based on the ballistic propagation of the wave packet centred in the linear region of the dispersion relation by means of the on-site magnetic field. At the same time, the wave packet width, modulated by the inter-site couplings at the chain ends, whose values are found via a carefully designed genetic algorithm, is constrained mostly in the linear region of the dispersion relation. Our coupling scheme is shown to hold for arbitrary values of the next-nearest inter-site coupling and can be straightforwardly applied to longer-range coupling schemes.