$\mathsf{BQP/qpoly}$ be the class of problems solvable in quantum polynomial time, given a polynomial-size quantum advice state $\left\vert \psi_{n}\right\rangle $ that depends only on the input length $n$. Then recently I showed that $\mathsf{NP}\not \subset \mathsf{BQP/qpoly}$ relative to an oracle [@aar:adv].  Intuitively, even if the state $\left\vert \psi
_{n}\right\rangle $ encoded the solutions to every 3SAT instance of size $n$, only a miniscule fraction of that information could be extracted by measuring $\left\vert \psi_{n}\right\rangle $, at least within the black-box model that we know how to analyze.  The proof uses the polynomial technique of Beals et al. [@bbcmw] to prove a so-called *direct product theorem*, which upper-bounds the probability of solving many database search problems simultaneously.  It then shows that this direct product theorem could be violated, if the search problem were efficiently solvable using quantum advice.

The Quantum Adiabatic Algorithm\[ADIABAT\]
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At this point, some readers may be getting impatient with the black-box model.  After all, $\mathsf{NP}$-complete problems are *not* black boxes, and classical algorithms such as backtrack search do exploit their structure.  Why couldn’t a quantum algorithm do the same?  A few years ago, Farhi et al. [@fggllp] announced a new *quantum adiabatic algorithm*, which can be seen 