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Related papers: QMIP = MIP*

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We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…

Quantum Physics · Physics 2018-06-01 Joseph Fitzsimons , Zhengfeng Ji , Thomas Vidick , Henry Yuen

This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…

Quantum Physics · Physics 2016-05-25 Hirotada Kobayashi , François Le Gall , Harumichi Nishimura

The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset…

Quantum Physics · Physics 2025-08-29 Abuzer Yakaryılmaz

Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical…

Quantum Physics · Physics 2019-03-01 Yusuke Kinoshita

We investigate two resources whose effects on quantum interactive proofs remain poorly understood: the promise of unentanglement, and the verifier's ability to condition on an intermediate measurement, which we call post-measurement…

Quantum Physics · Physics 2025-09-22 Sabee Grewal , William Kretschmer

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output…

Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…

Quantum Physics · Physics 2015-08-25 Harumichi Nishimura , Tomoyuki Yamakami

We introduce two models of space-bounded quantum interactive proof systems, ${\sf QIPL}$ and ${\sf QIP_{\rm U}L}$. The ${\sf QIP_{\rm U}L}$ model, a space-bounded variant of quantum interactive proofs (${\sf QIP}$) introduced by Watrous (CC…

Quantum Physics · Physics 2025-07-30 François Le Gall , Yupan Liu , Harumichi Nishimura , Qisheng Wang

Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation…

Computational Complexity · Computer Science 2017-11-15 Jing Chen , Samuel McCauley , Shikha Singh

In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a…

Computational Complexity · Computer Science 2007-05-23 John Watrous

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

We show that the value of a general two-prover quantum game cannot be computed by a semi-definite program ofvpolynomial size (unless P=NP), a method that has been successful in more restricted quantum games. More precisely, we show that…

Quantum Physics · Physics 2007-05-23 Julia Kempe , Thomas Vidick

In 2020, a landmark result by Ji, Natarajan, Vidick, Wright, and Yuen showed that MIP*, the class of languages that can be decided by a classical verifier interacting with multiple computationally unbounded provers sharing entanglement in…

Quantum Physics · Physics 2025-10-09 Junqiao Lin

Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP}…

Quantum Physics · Physics 2026-04-15 Scott Aaronson , Anand Natarajan , Avishay Tal , Agi Villanyi

We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update…

Quantum Physics · Physics 2009-08-03 Rahul Jain , Zhengfeng Ji , Sarvagya Upadhyay , John Watrous

We consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular,…

Quantum Physics · Physics 2025-07-22 Matthias C. Caro , Jens Eisert , Marcel Hinsche , Marios Ioannou , Alexander Nietner , Ryan Sweke

Many applications of quantum information processing (QIP) require distribution of quantum states in networks, both within and between distant nodes. Optical quantum states are uniquely suited for this purpose, as they propagate with…

Quantum Physics · Physics 2020-02-20 Junxin Chen , Massimiliano Rossi , David Mason , Albert Schliesser

We show that, for any language in NP, there is an entanglement-resistant constant-bit two-prover interactive proof system with a constant completeness vs. soundness gap. The previously proposed classical two-prover constant-bit interactive…

Quantum Physics · Physics 2007-07-13 Richard Cleve , Dmitry Gavinsky , Rahul Jain

Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…

Quantum Physics · Physics 2021-11-12 Gregory Rosenthal , Henry Yuen

In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…

Quantum Physics · Physics 2024-03-21 Anand Natarajan , Chinmay Nirkhe