This paper studies whether quantum proofs are more powerful than
classical proofs, or in complexity terms, whether QMA=QCMA. We prove
two results about this question. First, we give a "quantum oracle
separation" between QMA and QCMA. More concretely, we show that any
quantum algorithm needs order sqrt(2^n/(m+1)) queries to find ... more >>>

We consider the \emph{Hidden Subgroup} in the context of quantum \emph{Ordered Binary Decision Diagrams}.
We show several lower bounds for this function.
In this paper we also consider a slightly more general definition of the
hidden subgroup problem (in contrast to that in \cite{khashsp1}). It turns out that ... more >>>

This mini-course will introduce participants to an exciting frontier for quantum computing theory: namely, questions involving the computational complexity of preparing a certain quantum state or applying a certain unitary transformation. Traditionally, such questions were considered in the context of the Nonabelian Hidden Subgroup Problem and quantum interactive proof systems, ... more >>>

We show that the Hidden Subgroup Problem for black-box groups is in $\mathrm{BPP}^\mathrm{MKTP}$ (where $\mathrm{MKTP}$ is the Minimum $\mathrm{KT}$ Problem) using the techniques of Allender et al (2018). We also show that the problem is in $\mathrm{ZPP}^\mathrm{MKTP}$ provided that there is a \emph{pac overestimator} computable in $\mathrm{ZPP}^\mathrm{MKTP}$ for the logarithm ... more >>>