Pretty good state transfer via adaptive quantum error correction

TL;DR

This paper demonstrates how adaptive quantum error correction can significantly improve quantum state transfer fidelity in 1D spin chains, even with disorder, by analyzing the quantum channel and optimizing error correction protocols.

Contribution

It introduces an adaptive QEC protocol for pretty good state transfer in 1D spin chains, with analytical and numerical validation under ideal and disordered conditions.

Findings

Adaptive QEC enhances state transfer fidelity.

Disorder affects the effectiveness of QEC, with a threshold identified.

Modified QEC protocols can maintain high fidelity for small disorder strengths.

Abstract

We examine the role of quantum error correction (QEC) in achieving pretty good quantum state transfer over a class of $1$-d spin Hamiltonians. Recasting the problem of state transfer as one of information transmission over an underlying quantum channel, we identify an adaptive QEC protocol that achieves pretty good state transfer. Using an adaptive recovery and approximate QEC code, we obtain explicit analytical and numerical results for the fidelity of transfer over ideal and disordered $1$-d Heisenberg chains. In the case of a disordered chain, we study the distribution of the transition amplitude, which in turn quantifies the stochastic noise in the underlying quantum channel. Our analysis helps us to suitably modify the QEC protocol so as to ensure pretty good state transfer for small disorder strengths and indicates a threshold beyond which QEC does not help in improving the fidelity of state transfer.