We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise permutations. In all cases, the sizes of the objects are optimal up to polynomial overhead. ... more >>>

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 >>>