Proving lower bounds against depth-$2$ linear threshold circuits (a.k.a. $THR \circ THR$) is one of the frontier questions in complexity theory. Despite tremendous effort, our best lower bounds for $THR \circ THR$ only hold for sub-quadratic number of gates, which was proven a decade ago by Tamaki (ECCC TR16) and ... more >>>

A central goal in average-case complexity is to understand how average-case hardness can be amplified to near-optimal hardness. Classical results such as Yao’s XOR lemma establish this principle for Boolean functions, but these techniques typically apply only to artificially constructed functions, rather than to natural computational problems. In this work, ... more >>>

Zero-knowledge codes, introduced by Decatur, Goldreich, and Ron (ePrint 1997), are error-correcting codes in which few codeword symbols reveal no information about the encoded message, and have been extensively used in cryptographic constructions. Quantum CSS codes, introduced by Calderbank and Shor (Phys. Rev. A 1996) and Steane (Royal Society A ... more >>>