English
Related papers

Related papers: Zero-knowledge proof systems for QMA

200 papers

In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the…

Quantum Physics · Physics 2014-04-29 Adam D. Bookatz

The complexity class QMA is the quantum analog of the classical complexity class NP. The functional analogs of NP and QMA, called functional NP (FNP) and functional QMA (FQMA), consist in either outputting a (classical or quantum) witness,…

Quantum Physics · Physics 2021-02-09 Serge Massar , Miklos Santha

This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of…

Quantum Physics · Physics 2007-05-23 Hirotada Kobayashi

We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…

Quantum Physics · Physics 2018-06-25 Anne Broadbent

A new interactive quantum zero-knowledge protocol for identity authentication implementable in currently available quantum cryptographic devices is proposed and demonstrated. The protocol design involves a verifier and a prover knowing a…

We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…

Quantum Physics · Physics 2022-10-17 Marcel Dall'Agnol , Tom Gur , Subhayan Roy Moulik , Justin Thaler

Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of…

Quantum Physics · Physics 2024-03-01 Fernando Granha Jeronimo , Pei Wu

Zero-knowledge proofs allow verification of computations without revealing private information. However, existing systems require memory proportional to the computation size, which has historically limited use in large-scale applications…

Cryptography and Security · Computer Science 2025-09-18 Logan Nye

A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…

Quantum Physics · Physics 2022-09-21 Zhenning Liu , Alexandru Gheorghiu

We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to…

Quantum Physics · Physics 2015-05-28 Zhengfeng Ji

QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…

Quantum Physics · Physics 2016-03-02 Tomoyuki Morimae , Daniel Nagaj , Norbert Schuch

In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…

Quantum Physics · Physics 2016-11-25 Hugue Blier , Alain Tapp

The quantum PCP (QPCP) conjecture states that all problems in QMA, the quantum analogue of NP, admit quantum verifiers that only act on a constant number of qubits of a polynomial size quantum proof and have a constant gap between…

Quantum Physics · Physics 2016-03-09 Alex B. Grilo , Iordanis Kerenidis , Attila Pereszlényi

Complexity theory typically focuses on the difficulty of solving computational problems using classical inputs and outputs, even with a quantum computer. In the quantum world, it is natural to apply a different notion of complexity, namely…

Quantum Physics · Physics 2025-04-07 Hugo Delavenne , François Le Gall , Yupan Liu , Masayuki Miyamoto

We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems…

Quantum Physics · Physics 2007-05-23 Dominik Janzing , Pawel Wocjan , Thomas Beth

The round complexity of interactive proof systems is a key question of practical and theoretical relevance in complexity theory and cryptography. Moreover, results such as QIP = QIP(3) (STOC'00) show that quantum resources significantly…

Quantum Physics · Physics 2024-05-29 Alex B. Grilo , Philippe Lamontagne

We initiate the study of relativistic zero-knowledge quantum proof of knowledge systems with classical communication, formally defining a number of useful concepts and constructing appropriate knowledge extractors for all the existing…

Quantum Physics · Physics 2024-12-18 Kaiyan Shi , Kaushik Chakraborty , Wen Yu Kon , Omar Amer , Marco Pistoia , Charles Lim

In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that…

Quantum Physics · Physics 2007-05-23 John Watrous

We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…

Quantum Physics · Physics 2017-05-24 Richard Jozsa , Sergii Strelchuk

Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is…

Quantum Physics · Physics 2007-05-23 Jose Claudio do Nascimento , Rubens Viana Ramos