 
Summary: A Full Characterization of Quantum Advice
Scott Aaronson #
MIT
Andrew Drucker +
MIT
ABSTRACT
We prove the following surprising result: given any quan
tum state # on n qubits, there exists a local Hamiltonian
H on poly (n) qubits (e.g., a sum of twoqubit interactions),
such that any ground state of H can be used to simulate
# on all quantum circuits of fixed polynomial size. In
terms of complexity classes, this implies that BQP/qpoly #
QMA/poly, which supersedes the previous result of Aaronson
that BQP/qpoly # PP/poly. Indeed, we can exactly charac
terize quantum advice, as equivalent in power to untrusted
quantum advice combined with trusted classical advice.
Proving our main result requires combining a large num
ber of previous toolsincluding a result of Alon et al. on
learning of realvalued concept classes, a result of Aaron
son on the learnability of quantum states, and a result of
