Saved in:
Bibliographic Details
Main Authors: Aaronson, Scott, Harris, Phillip, Witteveen, Freek
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.21131
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909833626648576
author Aaronson, Scott
Harris, Phillip
Witteveen, Freek
author_facet Aaronson, Scott
Harris, Phillip
Witteveen, Freek
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_21131
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Limits to black-box amplification in QMA
Aaronson, Scott
Harris, Phillip
Witteveen, Freek
Quantum Physics
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.
title Limits to black-box amplification in QMA
topic Quantum Physics
url https://arxiv.org/abs/2509.21131