The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective
Abstract
In this paper I revisit my 2006 conjecture on correlated errors in entangled physical qubits, originally proposed as a potential obstruction to quantum fault tolerance. The conjecture asserts that, in any physical implementation of a quantum computer, the effective noise channel acting on entangled physical qubits contains a joint fully depolarizing component, with a rate comparable to that of two-qubit gate errors. This hypothesized structural constraint goes beyond standard noise models and, if valid, would pose a significant challenge to scalable quantum fault tolerance. The conjecture remains open, but recent advances in experimental quantum computing bring it within reach of empirical testing on current devices. I also discuss two related directions in my critical study of quantum computation: the role of noise sensitivity and computational complexity in noisy intermediate-scale quantum systems, and the statistical analysis of experimental claims of quantum advantage. Finally, since this paper is written for a volume honoring Yuri Gurevich, I include some reflections on the ways in which my scientific and personal trajectory became intertwined with Yuri's.
Related
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BibTeX
@misc{kalai2026fully,
title = {{The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective}},
author = {Gil Kalai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33508},
eprint = {2609.33508},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33508},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective
AU - Gil Kalai
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33508
UR - https://arxiv.org/abs/2609.33508
AB - In this paper I revisit my 2006 conjecture on correlated errors in entangled physical qubits, originally proposed as a potential obstruction to quantum fault tolerance. The conjecture asserts that, in any physical implementation of a quantum computer, the effective noise channel acting on entangled physical qubits contains a joint fully depolarizing component, with a rate comparable to that of two-qubit gate errors. This hypothesized structural constraint goes beyond standard noise models and, if valid, would pose a significant challenge to scalable quantum fault tolerance. The conjecture remains open, but recent advances in experimental quantum computing bring it within reach of empirical testing on current devices. I also discuss two related directions in my critical study of quantum computation: the role of noise sensitivity and computational complexity in noisy intermediate-scale quantum systems, and the statistical analysis of experimental claims of quantum advantage. Finally, since this paper is written for a volume honoring Yuri Gurevich, I include some reflections on the ways in which my scientific and personal trajectory became intertwined with Yuri's.
ER -