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A Full Characterization of Quantum Advice Scott Aaronson #

Summary: A Full Characterization of Quantum Advice
Scott Aaronson #
Andrew Drucker +
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 tools---including 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


Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)


Collections: Physics; Computer Technologies and Information Sciences