Orientation-dependent Pauli noise in one-dimensional discrete-time quantum walks
Abstract
Discrete-time quantum walks exhibit ballistic spreading that is highly sensitive to decoherence. We study the long-time dynamics of a one-dimensional discrete-time quantum walk under Pauli noise acting on the coin. Choosing the unitary coin such that its invariant Bloch-sphere axis is orthogonal to the axis fixed by the conditional shift, we identify the distinct effects of noise aligned with either dynamical axis or orthogonal to both. Using a Fourier-space Pauli-superoperator formalism, we derive expressions for the first two position moments and long-time asymptotics for X-, Y-, Z-, and depolarizing noise. All channels induce a crossover from ballistic to diffusive spreading, with a second moment growing linearly at long times. The approach to this regime is channel dependent: it is exponentially fast for X-, Z-, and depolarizing noise, but algebraic, with a leading t−1/2 correction, for Y-noise. The position distributions retain distinct finite-noise signatures, including a Gaussian-like profile with a central depression for Y-noise. In the maximal-noise limit, depolarizing, Y-, and Z-noise yield the classical binomial distribution for arbitrary initial coin states, whereas X-noise does so only when the initial state has no component along the noise axis. Thus, the quantum-to-classical transition is governed by the relative alignment of the noise, the coherent walk dynamics, and the initial state.
Related
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BibTeX
@misc{reynoso2026orientationdependent,
title = {{Orientation-dependent Pauli noise in one-dimensional discrete-time quantum walks}},
author = {Alejandro Contreras Reynoso and Adrian Ortega and Thomas Gorin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13392},
eprint = {2609.13392},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13392},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Orientation-dependent Pauli noise in one-dimensional discrete-time quantum walks
AU - Alejandro Contreras Reynoso
AU - Adrian Ortega
AU - Thomas Gorin
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13392
UR - https://arxiv.org/abs/2609.13392
AB - Discrete-time quantum walks exhibit ballistic spreading that is highly sensitive to decoherence. We study the long-time dynamics of a one-dimensional discrete-time quantum walk under Pauli noise acting on the coin. Choosing the unitary coin such that its invariant Bloch-sphere axis is orthogonal to the axis fixed by the conditional shift, we identify the distinct effects of noise aligned with either dynamical axis or orthogonal to both. Using a Fourier-space Pauli-superoperator formalism, we derive expressions for the first two position moments and long-time asymptotics for X-, Y-, Z-, and depolarizing noise. All channels induce a crossover from ballistic to diffusive spreading, with a second moment growing linearly at long times. The approach to this regime is channel dependent: it is exponentially fast for X-, Z-, and depolarizing noise, but algebraic, with a leading t^−1/2 correction, for Y-noise. The position distributions retain distinct finite-noise signatures, including a Gaussian-like profile with a central depression for Y-noise. In the maximal-noise limit, depolarizing, Y-, and Z-noise yield the classical binomial distribution for arbitrary initial coin states, whereas X-noise does so only when the initial state has no component along the noise axis. Thus, the quantum-to-classical transition is governed by the relative alignment of the noise, the coherent walk dynamics, and the initial state.
ER -