Quantum State Transfer: Protocols via Spin Chain Optimization and Construction

Extensive research has outlined the pivotal role of appropriate spectra in enabling quantum information transfer via spin chain mirror inversion. Through a combination of numerical and analytical methods, researchers have identified configurations of nearest-neighbor couplings and on-site energies that facilitate perfect or near-perfect state transfer (PST-PGST). One notably effective model, derived from an equidistant spectrum (Christandl et al.), relies on strongly inhomogeneous couplings across the sites while leaving local magnetic fields unaltered. Through the use of evolutionary numerical methods, specifically a tailored genetic algorithm, we have uncovered an alternative spectrum. This alternative spectrum yields high-fidelity transfer solely through modulation of on-site energies. This spectrum, up to an approximate number of sites, allows for complete homogeneity of the couplings, thereby simplifying experimental requirements.

We've also used a secondary numerical approach in an inverse eigenvalue method to provide an auxiliary analysis in distinguishing quasi-perfect state transfer (QPST) and PST, as well as highlighting the trade-offs for both. Through these analyses we may propose alternative prescriptions which offers potential advantages for experimental implementation while still aiming for perfect or near-perfect state transfer.