 
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
