Related papers: MAX 2-SAT with up to 108 qubits
To solve 3SAT instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
This paper builds on top of a paper we have published very recently, in which we have proposed a novel approach to prime factorization (PF) by quantum annealing, where 8,219,999=32,749x251 was the highest prime product we were able to…
Quantum chemistry is one of the most promising applications of quantum computers in the near future. For noisy intermediate-scale quantum devices, the quantum-classical hybrid framework based on the variational quantum eigensolver (VQE) has…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
There has been much recent interest in the satisfiability of random Boolean formulas. A random k-SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known…
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are…
The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric…
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…
With qubit measurement and control fidelities above the threshold of fault-tolerance, much attention is moving towards the daunting task of scaling up the number of physical qubits to the large numbers needed for fault tolerant quantum…
Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm. However, in general, we cannot embed all the logical variables of a…
Variational quantum algorithms are the centerpiece of modern quantum programming. These algorithms involve training parameterized quantum circuits using a classical co-processor, an approach adapted partly from classical machine learning.…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
We report the Atos Q-score for D-Wave's quantum devices, classical algorithms and hybrid quantum-classical solver. Computing the Q-score entails solving the Max-Cut problem for increasingly large graphs. This work presents the first…
A challenge for scaling up quantum processors using frequency-crowded, weakly anharmonic qubits is to drive individual qubits without causing leakage into non-computational levels of the others, while also minimizing the number of control…
This paper investigates the performance of quantum, classical, and hybrid solvers on the NP-hard Max-Cut and QUBO problems, examining their solution quality relative to the global optima and their computational efficiency. We benchmark the…
A recent Google study [Phys. Rev. X, 6:031015 (2016)] compared a D-Wave 2X quantum processing unit (QPU) to two classical Monte Carlo algorithms: simulated annealing (SA) and quantum Monte Carlo (QMC). The study showed the D-Wave 2X to be…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
The D-Wave quantum annealers make it possible to obtain high quality solutions of NP-hard problems by mapping a problem in a QUBO (quadratic unconstrained binary optimization) or Ising form to the physical qubit connectivity structure on…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…