We continue the study of the Stoquastic Local Hamiltonian problem, a physically motivated restriction of the $\QMA$-complete Local Hamiltonian problem \cite{KSV02}. For the $\beta$-gapped, frustration-free case, \citet{BBT06} showed that the problem is $\MA$-complete when $\beta= \frac{1}{\poly(n)}$. \citet{AG19} derandomized this algorithm and proved membership in $\NP$ for constant gap $\beta = ... more >>>

In this work we give a randomized blackbox polynomial identity testing (PIT) algorithm for constant-depth homogeneous noncommutative circuits, with poly-logarithmic time complexity in the circuit size. In fact, we show that the polynomial computable by such a depth-$(\Delta-1)$ circuit of size $s$ cannot be a polynomial identity for the $O(\log ... more >>>

We present a methodology for constructing interactive proof systems.
This methodology, which is implicit in prior works, consists of reducing the original claim to an iteratively generated sequence of claims such that each claim is (interactively) generated based on the prior claim.
Viewing each of these interactive generation ... more >>>