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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 two-qubit 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


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


Collections: Physics; Computer Technologies and Information Sciences