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arXiv:2508.08182 · New Journal of Physics

Fast and efficient long-distance quantum state transfer in long-range spin- 1 2 models

F Faria, Chad C. Nelmes, Tony J. G. Apollaro, Timothy P. Spiller, Irene D’Amico

Published Nov 26, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract Quantum state transfer (QST) is investigated beyond the nearest-neighbour coupling scheme in long spin- 1 2 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.

DOI
10.1088/1367-2630/ae249f

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We identify different regimes of quantum state transfer in long-range coupled spin-12\frac{1}{2}21​ systems, where naturally occurring power-law interactions enable rapid, high-fidelity transfer with minimal engineering. Across a broad range of interaction profiles, from effectively nearest-neighbour coupling to Coulomb interactions, we show how long-range connectivity fundamentally reshapes the mechanisms underlying information propagation within such systems. For effectively short-range interactions, transfer follows familiar ballistic transfer dynamics: an initially localised excitation spreads across many eigenmodes concentrated within the approximately linear region of the spectrum, enabling robust wavepacket motion. In contrast, increasing long-distance interactions via lowering the power-law exponent ααα (α=1−2α=1-2α=1−2) drives a striking transformation, where the initial state becomes confined to progressively fewer eigenmodes, ultimately reducing the dynamics to the coherent participation of only a few states corresponding to the highest eigenenergies. This spectral localization gives rise to emergent long-range oscillations between distant sites, revealing a distinct -- and faster -- transfer mechanism arising from the intrinsic structure of long-range quantum interactions rather than from full-system engineering pathways.
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Abstract Designing a good transfer channel for arbitrary quantum states in spin chains implies optimising a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles the state prepared at the beginning of the transfer protocol. When averaged over all the possible initial states, the figure of merit quantifies the quality of the protocol. There are proposals for optimising a given Hamiltonian to accomplish a particular task. The transfer of quantum states is one of them. In particular, we consider the design of Heisenberg spin chains using a genetic algorithm. This very efficient algorithm allows us to study different properties of Hamiltonians with good to excellent transfer ability. Using an evolutionary population method results in exchange coefficient strengths that change abruptly from site to site, which could hinder implementing an actual physical system with such exchange coefficients. By modifying the cost function, we obtain Hamiltonians with exchange coefficients varying smoothly along the chain length without compromising their transfer ability concerning the rough ones. Besides, both kinds of chain Hamiltonians show similar robustness against static disorder. By studying the statistical properties of the eigenvalues of Hamiltonians with varying transfer abilities, we determine the ensemble of random matrices to which the spectra belong.
Abstract Quantum state transfer (QST) is a fundamental requirement for scalable quantum computation, where fast and reliable communication between distant subsystems is essential. In this work, we present a protocol for QST in linear Ising chains. Starting from a perfect state transfer scheme via a Heisenberg Hamiltonian with inhomogeneous couplings, we adapt it for architectures implementing the transverse-field Ising model by encoding the information in domain walls. The resulting linear Ising chain makes quantum transport experiments accessible to many platforms for analog quantum simulation. We test the protocol for 1-, 2-, and 3- spin states, obtaining high transfer fidelities of up to 0.99 and study the accuracy dependence on the domain wall approximation. These results are the first step in paving the way for an experimental implementation of the protocol.