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arXiv · 2010.15281

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

A. R. C. Buarque·W. S. Dias
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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.

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A. R. C. Buarque, W. S. Dias. 2020-10-28. Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics. https://doi.org/10.1103/physreva.103.042213

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