The strength of weak coupling

TL;DR

This paper rigorously proves that weak coupling in quantum transport can enhance state transfer and overcome localization, with implications for quantum search and speedups.

Contribution

It provides a rigorous mathematical proof of the beneficial effects of weak coupling in quantum transport, using elementary perturbation theory methods.

Findings

Weak coupling enables high-fidelity quantum state transfer.

Weak coupling helps circumvent Anderson localization.

Weak coupling can speed up quantum search processes.

Abstract

A paradoxical idea in quantum transport is that attaching weakly-coupled edges to a large base graph creates high-fidelity quantum state transfer. We provide a mathematical treatment that rigorously prove this folklore idea. Our proofs are elementary and build upon the Feshbach-Schur method from perturbation theory. We also show the idea is effective in circumventing Anderson localization in spin chains and finding speedups in hitting times useful for quantum search.