Distinct Modes of Quantum Information Transfer in Power-Law Long-Range Spin Networks

This paper investigates how naturally occurring power-law long-range interactions in spin-1/2 chains influence quantum state transfer across different interaction profiles. The authors examine whether unmodulated or minimally engineered power-law spin networks can achieve high-fidelity state transfer within feasible coherence times as system size scales. To answer this, they use genetic algorithms to optimize boundary site positions and local magnetic fields in spin chains ranging from 4 to 100 sites, covering interaction decay exponents from alpha = 1 (Coulomb-like) to alpha = 10 (nearest-neighbour-like).

By analyzing the energy spectra and dynamical evolution of optimized chains, the study reveals a fundamental transition in how quantum information propagates. For effectively short-range interactions at higher alpha, transfer follows standard ballistic dynamics where an initial excitation spreads across numerous eigenmodes located in an approximately linear region of the spectrum. Conversely, lowering the power-law exponent towards alpha = 1 strongly concentrates the initial state onto only a few eigenmodes at the highest energies. This spectral localization produces much faster transfer times via emergent long-range oscillations directly between distant end sites without requiring full-system engineering.

As the decay exponent increases from alpha = 1.0 to alpha = 3.0, the optimal transfer time grows monotonically because a wider wavepacket of energy eigenstates begins to participate in the dynamics. A transitional region between alpha = 1.0 and alpha = 2.0 marks the crossover from few-mode coherent oscillations to ballistic wavepacket motion. Crucially, optimizing only a few boundary sites and local magnetic fields is sufficient to achieve near-perfect average transfer fidelity exceeding 0.999 across all explored power-law profiles.