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arXiv · 2509.21131

Limits to black-box amplification in QMA

Scott Aaronson·Phillip Harris·Freek Witteveen
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Abstract

We study the limitations of black-box amplification in the quantum complexity class QMA. Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result (Jeffery and Witteveen, 2025) shows that completeness can in fact be amplified to be doubly exponentially close to 1. We prove that this is optimal for black-box procedures: we provide a quantum oracle relative to which no QMA verification procedure using polynomial resources can achieve completeness closer to 1 than doubly exponential, or a soundness which is super-exponentially small. This is proven by using techniques from complex approximation theory, to make the oracle separation from (Aaronson, 2008), between QMA and QMA with perfect completeness, quantitative.

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Scott Aaronson, Phillip Harris, Freek Witteveen. 2025-09-25. Limits to black-box amplification in QMA. https://arxiv.org/abs/2509.21131

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