Related papers: Short Multi-Prover Quantum Proofs for SAT without …

This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is Omega(1/n polylog(n)). This…

We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also…

This paper studies multiple-proof quantum Merlin-Arthur (QMA) proof systems in the setting when the completeness-soundness gap is small. Small means that we only lower-bound the gap with an inverse-exponential function of the input length,…

The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give…

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…

What happens if in QMA the quantum channel between Merlin and Arthur is noisy? It is not difficult to show that such a modification does not change the computational power as long as the noise is not too strong so that errors are…

We present three contributions to the understanding of QMA with multiple provers: 1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap Omega(1/N^2). Our improvement is achieved…

This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical…

We show that the class QAM does not change even if the verifier's ability is restricted to only single-qubit measurements. To show the result, we use the idea of the measurement-based quantum computing: the verifier, who can do only…

We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with…

Quantum Merlin-Arthur proof systems are believed to be stronger than both their classical counterparts and ``stand-alone'' quantum computers when Arthur is assumed to operate in $\Omega(\log n)$ space. No hint of such an advantage over…

Can one considerably shorten a proof for a quantum problem by using a protocol with a constant number of unentangled provers? We consider a frustration-free variant of the QCMA-complete Ground State Connectivity (GSCON) problem for a system…

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve $\NP$-complete problems given a "short" quantum proof; more precisely, $\NP\subseteq…

We study a variant of QMA where quantum proofs have no relative phase (i.e. non-negative amplitudes, up to a global phase). If only completeness is modified, this class is equal to QMA [arXiv:1410.2882]; but if both completeness and…

We find a modification to QMA where having one quantum proof is strictly less powerful than having two unentangled proofs, assuming EXP $\ne$ NEXP. This gives a new route to prove QMA(2) = NEXP that overcomes the primary drawback of a…

We present an efficient proof system for Multipoint Arithmetic Circuit Evaluation: for every arithmetic circuit $C(x_1,\ldots,x_n)$ of size $s$ and degree $d$ over a field ${\mathbb F}$, and any inputs $a_1,\ldots,a_K \in {\mathbb F}^n$,…

We define and study a variant of QMA (Quantum Merlin Arthur) in which Arthur can make multiple non-collapsing measurements to Merlin's witness state, in addition to ordinary collapsing measurements. By analogy to the class PDQP defined by…

We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…

We give a simpler proof of one of the results of Kobayashi, Le Gall, and Nishimura [arXiv:1210.1290v2], which shows that any QMA protocol can be converted to a one-sided error protocol, in which Arthur and Merlin initially share a constant…

Entanglement properties of IBM Q 53 qubit quantum computer are carefully examined with the noisy intermediate-scale quantum (NISQ) technology. We study GHZ-like states with multiple qubits (N=2 to N=7) on IBM Rochester and compare their…