We give a simplified, self-contained proof of OpenAI's parity lower bound for constant-depth quantum circuits with arbitrary one-qubit gates, unbounded-arity Toffoli gates, and polynomially many ancillas. The proof establishes product-projection localization and uses it to bound the parity Fourier coefficient of the acceptance probability. We remove one circuit layer directly, ... more >>>

Hao, Huang, and Liu (STOC'26) recently showed that optimal quantum query complexity may require large workspace even for short-output problems, and asked whether a quantum query advantage over classical computation can itself require space. We resolve this question by exhibiting an explicit total Boolean function with quantum query complexity $Q=\widetilde{\Theta}(M)$, ... more >>>

We study one-way quantum communication lower bounds for search problems.Unlike decision problems, search problems can have many valid outputs, which pose a fundamental barrier to standard quantum lower-bound techniques. We overcome this by developing a novel method based on matrix discrepancy, which allows us to bound the output measurements of ... more >>>