The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective

Gil Kalai

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arXiv · 2609.33508

The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective

Gil Kalai

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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.

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Gil Kalai. 2026-09-27. The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective. https://arxiv.org/abs/2609.33508

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