Taking Advantage of Noise in Distributed Random Quantum Circuits
Abstract
Adding noise can make a random quantum circuit look faster without making its unitary dynamics more random. This distinction is especially relevant in modular processors, where local gates randomize each core and scarce inter-core communication must spread that randomness across the full device. In this paper, we study this problem with a reduced second-moment transfer-matrix theory for Pauli second moments in distributed random circuits affected by the amplitude-damping, depolarizing, and dephasing noise channels. The key step is to resolve the noisy spectrum into two branches: a radial branch, describing dissipative loss of non-identity Pauli weight, and an angular branch, describing Haar-like mixing within the surviving nontrivial sector. This separation gives a simple weak-noise criterion: noise is useful for angular randomization only when it suppresses the longitudinal Bloch component more strongly than the transverse plane. Among the three channels considered, this selects amplitude damping as the only locally favorable case, while depolarizing noise is neutral and dephasing is dominated by radial loss. For multicore architectures, we derive a universal first-order law for radial leakage and track the angular branch numerically across different channels, topologies, and core partitions. The results reveal narrow windows of genuine noise-assisted Haar mixing, most clearly for amplitude damping, but rule out a generic speed-up by noise. The framework therefore distinguishes useful noisy randomization from mere dissipation.
Related
- Towards verifiable quantum advantage with random circuits: Observables that survive concentration
- Quantum Advantage for Distributed Symmetry Breaking
- Experimentally Testable Quantum Advantage in Shallow Circuits
- Structural Conditions for Distributed Quantum Advantage
- Parallel classical simulation of noisy shallow circuits: no quantum advantage in 1D
BibTeX
@misc{montes2026taking,
title = {{Taking Advantage of Noise in Distributed Random Quantum Circuits}},
author = {J. Montes and F. Borondo and Gabriel G. Carlo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11898},
eprint = {2609.11898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11898},
}
RIS
TY - UNPB
TI - Taking Advantage of Noise in Distributed Random Quantum Circuits
AU - J. Montes
AU - F. Borondo
AU - Gabriel G. Carlo
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11898
UR - https://arxiv.org/abs/2609.11898
AB - Adding noise can make a random quantum circuit look faster without making its unitary dynamics more random. This distinction is especially relevant in modular processors, where local gates randomize each core and scarce inter-core communication must spread that randomness across the full device. In this paper, we study this problem with a reduced second-moment transfer-matrix theory for Pauli second moments in distributed random circuits affected by the amplitude-damping, depolarizing, and dephasing noise channels. The key step is to resolve the noisy spectrum into two branches: a radial branch, describing dissipative loss of non-identity Pauli weight, and an angular branch, describing Haar-like mixing within the surviving nontrivial sector. This separation gives a simple weak-noise criterion: noise is useful for angular randomization only when it suppresses the longitudinal Bloch component more strongly than the transverse plane. Among the three channels considered, this selects amplitude damping as the only locally favorable case, while depolarizing noise is neutral and dephasing is dominated by radial loss. For multicore architectures, we derive a universal first-order law for radial leakage and track the angular branch numerically across different channels, topologies, and core partitions. The results reveal narrow windows of genuine noise-assisted Haar mixing, most clearly for amplitude damping, but rule out a generic speed-up by noise. The framework therefore distinguishes useful noisy randomization from mere dissipation.
ER -