Related papers: Quantum interactive proofs with weak error bounds
In this paper, we introduce a new public quantum interactive proof system and the first quantum alternating Turing machine: qAM proof system and qATM, respectively. Both are obtained from their classical counterparts (Arthur-Merlin proof…
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…
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 finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive…
This paper proves one of the open problem posed by Beigi et al. in arXiv:1004.0411v2. We consider quantum interactive proof systems where in the beginning the verifier and prover send messages to each other with the combined length of all…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…
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,…
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…
Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show…
Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated…
$\text{MIP}^\ast$ 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 computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little…
This paper considers three variants of quantum interactive proof systems in which short (meaning logarithmic-length) messages are exchanged between the prover and verifier. The first variant is one in which the verifier sends a short…
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 systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
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…
This article shows that PSPACE not equal EXP. A simple but novel proof technique has been used to separate these two classes. Whether an arbitrary Turing machine accepts an input when the running time is limited has been computed in this…
Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus…
This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that…