Finding Traps in Non-linear Spin Arrays

TL;DR

This paper investigates how non-linear spin arrays, with multiple spins at some sites, differ from linear chains in quantum state transfer, and proposes methods to estimate system parameters and eliminate trapped excitations using only end data.

Contribution

It introduces a way to quantify differences between linear and pseudo-chains, and offers techniques to estimate system parameters and remove trapped excitations with minimal system access.

Findings

Quantifies differences between linear chains and pseudo-chains.

Provides methods to estimate number of spins and intra-block couplings.

Suggests ways to eliminate trapped excitations using end measurements.

Abstract

Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear structure. While this difference does not disturb the end-to-end dynamics of a single excitation, the evolution is significantly changed in other subspaces. Here we quantify the difference between a linear chain and a pseudo-chain, which have more than one spin at some site (block). We show how to estimate a number of all spins in the system and the intra-block coupling constants. We also suggest how it is possible to eliminate excitations trapped in such blocks, which may disturb the state transfer. Importantly, one uses only at-ends data and needs to be able to put the system to either the maximally magnetized or the maximally mixed state. This can obtained by controlling a global decoherence parameter, such as temperature.