NDLI: A full characterization of quantum advice

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A full characterization of quantum advice

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A full characterization of quantum advice

Content Provider	ACM Digital Library
Author	Drucker, Andrew Aaronson, Scott
Abstract	We prove the following surprising result: given any quantum state rho 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 rho on all quantum circuits of fixed polynomial size. In terms of complexity classes, this implies that BQP/qpoly is contained in QMA/poly, which supersedes the previous result of Aaronson that BQP/qpoly is contained in PP/poly. Indeed, we can exactly characterize quantum advice, as equivalent in power to untrusted quantum advice combined with trusted classical advice. Proving our main result requires combining a large number of previous tools -- including a result of Alon et al. on learning of real-valued concept classes, a result of Aaronson on the learnability of quantum states, and a result of Aharonov and Regev on "QMA+ super-verifiers" -- and also creating some new ones. The main new tool is a so-called majority-certificates lemma, which is closely related to boosting in machine learning, and which seems likely to find independent applications. In its simplest version, this lemma says the following. Given any set S of Boolean functions on n variables, any function f in S can be expressed as the pointwise majority of m=O(n) functions f1,.,fm in S, such that each fi is the unique function in S compatible with O(log\|S\|) input/output constraints.
Starting Page	131
Ending Page	140
Page Count	10
File Format	PDF
ISBN	9781450300506
DOI	10.1145/1806689.1806710
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-06-05
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Learning Karp-lipton theorem Compression Quantum computation Local hamiltonians Boosting Advice Nonuniform computation
Content Type	Text
Resource Type	Article

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