Succinct arguments for QMA from compiled nonlocal games

Speaker: Anand Natarajan , CSAIL MIT

Date: Tuesday, April 16, 2024

Time: 4:15 PM to 5:15 PM Note: all times are in the Eastern Time Zone

Public: Yes

Location: 32-G449

Event Type: Seminar

Room Description: Refreshments at 4:00pm

Host: Sam Hopkins, CSAIL MIT

Contact: Joanne Talbot Hanley, 617-253-6054, joanne@csail.mit.edu

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Reminders to: seminars@csail.mit.edu, theory-seminars@csail.mit.edu

Reminder Subject: TALK: TOC Seminar: Anand Natarajan, "Succinct arguments for QMA from compiled nonlocal games," Tuesday, April 16, 2024 at 4:15pm (Refreshments at 4:00pm) in 32-G449

Abstract: We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTO '22) also constructed a succinct classical argument system for QMA. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP* = RE in quantum complexity.

Joint work with Tony Metger (ETH Zurich) and Tina Zhang (MIT)

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Created by Joanne Talbot Hanley at Monday, April 08, 2024 at 8:56 AM.