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Related papers: Space-bounded quantum interactive proof systems

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We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by [AG17] showing a quantum-inspired interactive protocol ($\sf IP$) for $\sf PreciseBQP$ where the prover is only assumed to…

Quantum Physics · Physics 2021-11-08 Ayal Green , Guy Kindler , Yupan Liu

Multi Prover Interactive Proof systems (MIPs)were first presented in a cryptographic context, but ever since they were used in various fields. Understanding the power of MIPs in the quantum context raises many open problems, as there are…

Quantum Physics · Physics 2008-06-26 Michael Ben-Or , Avinatan Hassidim , Haran Pilpel

We present upper and lower bounds of the computational complexity of the two-way communication model of multiple-prover quantum interactive proof systems whose verifiers are limited to measure-many two-way quantum finite automata. We prove…

Quantum Physics · Physics 2015-08-25 Tomoyuki Yamakami

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

This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP,…

Computational Complexity · Computer Science 2007-05-23 Hirotada Kobayashi , Keiji Matsumoto

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum…

Quantum Physics · Physics 2016-11-17 Patrick Hayden , Kevin Milner , Mark M. Wilde

$\text{MIP}^\ast$ is the class of languages decidable by an efficient classical verifier interacting with multiple quantum provers that share entangled qubits but cannot communicate. Notably, $\text{MIP}^\ast$ was proved to equal…

Quantum Physics · Physics 2025-09-04 Itay Shalit

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 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

We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the…

Driven by exploring the power of quantum computation with a limited number of qubits, we present a novel complete characterization for space-bounded quantum computation, which encompasses settings with one-sided error (unitary coRQL) and…

Quantum Physics · Physics 2024-05-24 François Le Gall , Yupan Liu , Qisheng Wang

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

Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable…

Discrete Mathematics · Computer Science 2025-06-06 Michael Hartisch , Leroy Chew

Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial…

Quantum Physics · Physics 2013-11-08 Matthew McKague

We show that if a language $L$ admits a public-coin unambiguous interactive proof (UIP) with round complexity $\ell$, where $a$ bits are communicated per round, then the batch language $L^{\otimes k}$, i.e. the set of $k$-tuples of…

Computational Complexity · Computer Science 2025-10-23 Bonnie Berger , Rohan Goyal , Matthew M. Hong , Yael Tauman Kalai

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

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 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

Analysis and verification of quantum circuits are highly challenging, given the exponential dependence of the number of states on the number of qubits. For analytical derivation, we propose a new quantum polynomial representation (QPR) to…

Quantum Physics · Physics 2025-03-14 Yu-Ting Kao , Hao-Yu Lu , Yeong-Jar Chang , Darsen Lu

$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers,…

Quantum Physics · Physics 2015-12-08 Anand Natarajan , Thomas Vidick