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.

Quantum Physics (quant-ph); Computational Complexity (cs.CC)

arXiv:2609.33508 [quant-ph]

(or arXiv:2609.33508v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.33508 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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