Slepian Bounds on the Success Probability of Virtual Distillation

Abstract:Virtual distillation is a powerful near-term error-mitigation primitive, but it is also a spectral filter: it amplifies the dominant eigenvector component already present in the noisy density matrix. We show that, for a finite-band variational state, this filtering cannot create new concentration inside a set of accepted measurement outcomes. The asymptotic success probability after distillation is bounded by the leading eigenvalue of a Slepian concentration operator built from a specified variational band and that outcome window. Moreover, the number of robust high-success spectral components is limited by the Slepian active dimension. \rev{For bit-string outcome windows, an explicit Walsh-band realization has a Krawtchouk kernel on the Boolean hypercube. Finite-size noisy-QAOA calculations for 2-regular Max-Cut illustrate both the in-band improvement and the out-of-band failure modes predicted by the branch-resolved result.

arXiv:2608.21342 [quant-ph]

(or arXiv:2608.21342v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.21342 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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