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Abstract: We prove the following surprising result: given any quantum state rho on nqubits, there exists a local Hamiltonian H on polyn qubits e.g., a sum oftwo-qubit interactions, such that any ground state of H can be used tosimulate rho on all quantum circuits of fixed polynomial size. In terms ofcomplexity classes, this implies that BQP-qpoly is contained in QMA-poly, whichsupersedes the previous result of Aaronson that BQP-qpoly is contained inPP-poly. Indeed, we can exactly characterize quantum advice, as equivalent inpower 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, aresult of Aaronson on the learnability of quantum states, and a result ofAharonov and Regev on -QMA+ super-verifiers- and also creating some newones. The main new tool is a so-called majority-certificates lemma, which isclosely related to boosting in machine learning, and which seems likely to findindependent applications. In its simplest version, this lemma says thefollowing. Given any set S of Boolean functions on n variables, any function fin S can be expressed as the pointwise majority of m=On functions f1,

.,fmin S, such that each fi is the unique function in S compatible with Olog|S|input-output constraints.

Author: Scott Aaronson, Andrew Drucker

Source: https://arxiv.org/

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