QMA Lower Bounds for Batch Verification via Approximate Degree
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bun, Mark, Juvekar, Mandar, King, Samuel
Institutions: Boston University, Georgetown University
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168178476
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