We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.Our technique extends a result of Ambainis, based on the idea that successful computation of a function requires ``decoherence'' ... more >>>

A zap is a two-round, witness-indistinguishable protocol in which
the first round, consisting of a message from the verifier to the
prover, can be fixed ``once-and-for-all" and applied to any instance,
and where the verifier does not use any private coins.
We present a zap for every language in NP, ... more >>>

We show Minimum Vertex Cover NP-hard to approximate to within a factor
of 1.3606. This improves on the previously known factor of 7/6.

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