Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics

TL;DR

This paper investigates how short-time noise affects quantum walks on cycles, revealing new unstable regimes like self-focusing and breathing dynamics, and identifies conditions for stability and noise tolerance in quantum gates.

Contribution

It uncovers novel unstable regimes in quantum walks under noise and analyzes the stability of different quantum gates with respect to nonlinearities and noise tolerance.

Findings

Self-focusing and breathing dynamics emerge under certain noise conditions.

Stable regimes are favored with weak nonlinearities and large system size.

Pauli-Z gates are more noise-tolerant compared to Pauli-X and Hadamard gates.

Abstract

The sensitivity of quantum systems to external disturbances is a fundamental problem for the implementation of functional quantum devices, quantum information and computation. Based on remarkable experimental progress in optics and ultra-cold gases, we study the consequences of a short-time (instantaneous) noise while an intensity-dependent phase acquisition is associated with a qubit propagating on $N$-cycle. By employing quantum coherence measures, we report emerging unstable regimes in which hitherto unknown quantum walks arise, such as self-focusing and breathing dynamics. Our results unveil appropriate settings which favor the stable regime, with the asymptotic distribution surviving for weak nonlinearities and disappearing in the thermodynamic limit with $1/N$. The diagram showing the threshold between different regimes reveals the quantum gates close to Pauli-Z as more noise-tolerant. As we move towards the Pauli-X quantum gate, such aptness dramatically decreases and the threshold to self-focusing regime becomes almost unavoidable. Quantum gates close to Hadamard exhibit an unusual aspect, in which an increment of the nonlinear strength can remove the dynamics from self-focusing regime.