We study the implications of the existence of weak Zero-Knowledge (ZK) protocols for worst-case hard languages. These are protocols that have completeness, soundness, and zero-knowledge errors (denoted $\epsilon_c$, $\epsilon_s$, and $\epsilon_z$, respectively) that might not be negligible. Under the assumption that there are worst-case hard languages in NP, we show ... more >>>

We present efficient quantum circuits that implement high-dimensional unitary irreducible representations (irreps) of SU(n), where n>=2 is constant. For dimension N and error ?, the number of quantum gates in our circuits is polynomial in log(N) and log(1/?). Our construction relies on the Jordan-Schwinger representation, which allows us to realize ... more >>>

Guo, Saxena, and Sinhababu (TOC'18, CCC'18) defined a natural, approximative analog of the polynomial system satisfiability problem, which they called approximate polynomial satisfiability (APS). They proved algebraic and geometric properties of it and showed an NP-hardness lower bound and a PSPACE upper bound for it. They further established how the ... more >>>