QMA Lower Bounds for Batch Verification via Approximate Degree

Mark Bun; Mandar Juvekar; Samuel King

doi:10.4230/lipics.approx/random.2026.69

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arXiv · 2607.08888

QMA Lower Bounds for Batch Verification via Approximate Degree

Mark Bun·Mandar Juvekar·Samuel King

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Abstract

We study batch verification in QMA query and communication complexity, where the goal is to understand how the resources needed to verify $m$ copies of a Boolean function $f$ depend on $m$. We give a general technique for proving lower bounds on the witness-query tradeoff needed to batch verify a function $f$ in terms of its approximate degree. Applying this technique to an explicit family of DNF formulas $f$, we show that attempting to save even a constant factor on the witness length of the baseline approach to batch verifying $f$ necessitates a large polynomial increase in the query cost. We also obtain new lower bounds on the QMA query complexity of read-once CNF formulas and on the surjectivity and $k$-element distinctness functions. Our lower bounds also lift to give communication analogs of these results.

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BibTeX RIS

Mark Bun, Mandar Juvekar, Samuel King. 2026-07-09. QMA Lower Bounds for Batch Verification via Approximate Degree. https://doi.org/10.4230/lipics.approx%2Frandom.2026.69

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