Non-interactive zero-knowledge arguments for QMA, with preprocessing

by   Andrea Coladangelo, et al.

A non-interactive zero-knowledge (NIZK) proof system for a language L∈NP allows a prover (who is provided with an instance x ∈ L, and a witness w for x) to compute a classical certificate π for the claim that x∈ L such that π has the following properties: 1) π can be verified efficiently, and 2) π does not reveal any information about w, besides the fact that it exists (i.e. that x ∈ L). NIZK proof systems have recently been shown to exist for all languages in NP in the common reference string (CRS) model and under the learning with errors (LWE) assumption. We initiate the study of NIZK arguments for languages in QMA. Our first main result is the following: if LWE is hard for quantum computers, then any language in QMA has an NIZK argument with preprocessing. The preprocessing in our argument system consists of (i) the generation of a CRS and (ii) a single (instance-independent) quantum message from verifier to prover. The instance-dependent phase of our argument system involves only a single classical message from prover to verifier. Importantly, verification in our protocol is entirely classical, and the verifier needs not have quantum memory; its only quantum actions are in the preprocessing phase. Our second contribution is to extend the notion of a classical proof of knowledge to the quantum setting. We introduce the notions of arguments and proofs of quantum knowledge (AoQK/PoQK), and we show that our non-interactive argument system satisfies the definition of an AoQK. In particular, we explicitly construct an extractor which can recover a quantum witness from any prover who is successful in our protocol. We also show that any language in QMA has an (interactive) proof of quantum knowledge.



page 1

page 2

page 3

page 4


Non-interactive classical verification of quantum computation

In a recent breakthrough, Mahadev constructed an interactive protocol th...

Zero-Knowledge for QMA from Locally Simulatable Proofs

We provide several advances to the understanding of the class of Quantum...

Classically Verifiable (Dual-Mode) NIZK for QMA with Preprocessing

We propose three constructions of classically verifiable non-interactive...

Information-theoretically-sound non-interactive classical verification of quantum computing with trusted center

The posthoc verification protocol [J. F. Fitzsimons, M. Hajdušek, and T....

Multi-theorem (Malicious) Designated-Verifier NIZK for QMA

We present the first non-interactive zero-knowledge argument system for ...

Towards a quantum-inspired proof for IP = PSPACE

We explore quantum-inspired interactive proof systems where the prover i...

A Note on "New techniques for noninteractive zero-knowledge"

In 2012, Groth, et al. [J. ACM, 59 (3), 1-35, 2012] developed some new t...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.