quantum information in determining the power of $\mathsf{BQP/qpoly}$, a useful benchmark of comparison is the class $\mathsf{BQP/poly}$ of decision problems efficiently solvable by a quantum computer with $\operatorname*{poly}\left(  n\right) $ bits of *classical* advice. It is open whether $\mathsf{BQP/qpoly} =
\mathsf{BQP/poly}$.

A second approach studies the power of quantum *proof systems*, by analogy with the classical class $\mathsf{NP}$.  Kitaev (unpublished, 1999) defined the complexity class now called $\mathsf{QMA}$, for ‘Quantum Merlin-Arthur’. This is the class of decision problems for which a ‘yes’ answer can be proved by exhibiting a *quantum witness state* (or *quantum proof*) $\left\vert \psi\right\rangle $, on $\operatorname*{poly}\left(  n\right)  $ qubits, which is then checked by a skeptical polynomial-time quantum verifier. A natural benchmark class is $\mathsf{QCMA}$ (for ‘Quantum Classical Merlin-Arthur’), defined by Aharonov and Naveh [@an]. This is the class of decision problems for which a ‘yes’ answer can be checked by a *quantum* verifier who receives a *classical* witness.  Here the natural open question is whether $\mathsf{QMA} = \mathsf{QCMA}$.

In this paper we prove a new upper bound on $\mathsf{BQP/qpoly}$:

\[mainthm1\]$\mathsf{BQP/qpoly}\subseteq\mathsf{QMA/poly}$.

Previously Aaronson showed in [@aar:adv] that $\mathsf{BQP/qpoly}
\subseteq\mathsf{PP/poly}$, and showed in [@aar:learn] that $\mathsf{BQP/qpoly}$ is contained in the ‘heuristic’ class $\mathsf{HeurQMA/poly}$.  Theorem \[mainthm1\] supersedes both 