Year: 2013
Type: article
Abstract: We present three contributions to the understanding of QMA with multiple provers:• We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap Ω(N -2 ).Our improvement is achieved without the use of an instance with a constant soundness gap (i.e., without using a "PCP").• We give a tight soundness analysis of the protocol of [Chen and Drucker, ArXiV '10], thereby improving their result from a "monolithic" protocol where Θ( √ N) provers are needed in order to have any soundness gap, to a protocol with a smooth trade-off between the number of provers κ and a soundness gap Ω(κ 2 N -1 ), as long as κ ∈ Ω(log N). (And, when κ ∈ Θ( √ N), we recover the original parameters of Chen and Drucker.)• We make progress towards an open question of [Aaronson et al., ToC '09] about what kinds of NP-complete problems are amenable to "sublinear" multiple-prover QMA protocols, by observing that a large class of such examples can easily be derived from results already in the PCP literature -namely, at least the languages recognized by a non-deterministic RAMs in quasilinear time.
Authors: Alessandro Chiesa, Michael A. Forbes
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W1663554127