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We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum…

Quantum Physics · Physics 2023-12-11 Urmila Mahadev

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

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 study the limitations of black-box amplification in the quantum complexity class QMA. Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result…

Quantum Physics · Physics 2025-10-13 Scott Aaronson , Phillip Harris , Freek Witteveen

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

Quantum multiprover interactive proof systems with entanglement MIP* are much more powerful than its classical counterpart MIP (Babai et al. '91, Ji et al. '20): while MIP = NEXP, the quantum class MIP* is equal to RE, a class including the…

Quantum Physics · Physics 2025-02-18 Yangjing Dong , Honghao Fu , Anand Natarajan , Minglong Qin , Haochen Xu , Penghui Yao

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…

Determining the worst-case uncertainty added by a quantum circuit is shown to be computationally intractable. This is the problem of detecting when a quantum channel implemented as a circuit is close to a linear isometry, and it is shown to…

Quantum Physics · Physics 2010-06-02 Bill Rosgen

We present a simple quantum interactive proof (QIP) protocol using the quantum state teleportation (QST) and quantum energy teleportation (QET) protocols. QET is a technique that allows a receiver at a distance to extract the local energy…

Quantum Physics · Physics 2024-06-18 Kazuki Ikeda , Adam Lowe

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

We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques…

Quantum Physics · Physics 2011-08-05 Bill Rosgen

QMA and QCMA are possible quantum analogues of the complexity class NP. In QCMA the verifier is a quantum program and the proof is classical. In contrast, in QMA the proof is also a quantum state. We show that two known QMA-complete…

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

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

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…

Logic in Computer Science · Computer Science 2014-05-15 Thomas Gransden , Neil Walkinshaw , Rajeev Raman

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 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

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 consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to…

Quantum Physics · Physics 2008-04-11 Richard Cleve , William Slofstra , Falk Unger , Sarvagya Upadhyay

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

The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior…

Quantum Physics · Physics 2007-11-26 Julia Kempe , Hirotada Kobayashi , Keiji Matsumoto , Thomas Vidick