Related papers: On product, generic and random generic quantum sat…
A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a…
We present a simple, natural #P-complete problem. Let G be a directed graph, and let k be a positive integer. We define q(G;k) as follows. At each vertex v, we place a k-dimensional complex vector x_v. We take the product, over all edges…
The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold, $r_k n$. This causes a drastic reduction in the number of satisfying assignments,…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…
Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
We show that the Quantum State Distinguishability (QSD), which is a QSZK-complete problem, and the Quantum Circuit Distinguishability (QCD), which is a QIP-complete problem, can be solved by the verifier who can perform only single-qubit…
The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…
Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard…
An approach to the solution of NP-complete problems based on quantum computing and chaotic dynamics is proposed. We consider the satisfiability problem and argue that the problem, in principle, can be solved in polynomial time if we combine…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
In this paper we show that the performance of the quantum adiabatic algorithm is determined by phase transitions in underlying problem in the presence of transverse magnetic field $\Gamma$. We show that the quantum version of random…
We introduce a new model for the generation of random satisfiability problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt and Zecchina, which is a variant of the famous K-SAT model: it is extended to q-state…
The Quantum Satisfiability problem generalizes the Boolean satisfiability problem to the quantum setting by replacing classical clauses with local projectors. The Quantum Lov\'asz Local Lemma gives a sufficient condition for a Quantum…
Satisfiability is considered the canonical NP-complete problem and is used as a starting point for hardness reductions in theory, while in practice heuristic SAT solving algorithms can solve large-scale industrial SAT instances very…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…