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Related papers: MAX 2-SAT with up to 108 qubits

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The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…

Quantum Physics · Physics 2021-04-01 Marco Aldi , Niel de Beaudrap , Sevag Gharibian , Seyran Saeedi

Quantum annealing is a heuristic algorithm for solving combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware for implementing this algorithm. The current version of the D-Wave quantum annealer can solve…

Quantum Physics · Physics 2022-11-09 Shuntaro Okada , Masayuki Ohzeki , Shinichiro Taguchi

The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to…

Quantum Physics · Physics 2022-08-16 Sami Boulebnane , Ashley Montanaro

We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device.…

Quantum Physics · Physics 2015-04-03 Kristen L. Pudenz , Tameem Albash , Daniel A. Lidar

A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver…

Discrete Mathematics · Computer Science 2016-05-20 Gili Rosenberg , Mohammad Vazifeh , Brad Woods , Eldad Haber

As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of…

We consider the random 2-satisfiability problem, in which each instance is a formula that is the conjunction of m clauses of the form (x or y), chosen uniformly at random from among all 2-clauses on n Boolean variables and their negations.…

Combinatorics · Mathematics 2012-06-19 Béla Bollobás , Christian Borgs , Jennifer T. Chayes , Jeong Han Kim , David B. Wilson

We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a…

Quantum Physics · Physics 2021-02-08 Yanglin Hu , Zhelun Zhang , Biao Wu

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or QUBO (quadratic unconstrained binary optimization) form. Although such solutions are…

Quantum Physics · Physics 2022-10-27 Aaron Barbosa , Elijah Pelofske , Georg Hahn , Hristo N. Djidjev

We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and different objective: rather than looking for a state which…

Quantum Physics · Physics 2016-08-17 D. Wecker , M. B. Hastings , M. Troyer

The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…

Quantum Physics · Physics 2009-11-07 Tad Hogg

The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively…

Quantum Physics · Physics 2018-08-08 Tameem Albash , Daniel A. Lidar

The performance of a D-Wave Vesuvius quantum annealer was recently compared to a suite of classical algorithms on a class of constraint satisfaction instances based on frustrated loops. However, the construction of these instances leads the…

Quantum Physics · Physics 2015-09-07 Andrew D. King , Trevor Lanting , Richard Harris

Recently there has been intense interest in claims about the performance of the D-Wave machine. In this paper, we outline a simple classical model, and show that it achieves excellent correlation with published input-output behavior of the…

Quantum Physics · Physics 2014-05-05 Seung Woo Shin , Graeme Smith , John A. Smolin , Umesh Vazirani

It has been shown that Maximum Satisfiability (MaxSAT) problem instances can be effectively solved by partitioning the set of soft clauses into several disjoint sets. The partitioning methods can be based on clause weights (e.g.,…

Artificial Intelligence · Computer Science 2023-05-26 Pedro Orvalho , Vasco Manquinho , Ruben Martins

Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…

Combinatorics · Mathematics 2017-11-17 Amin Coja-Oghlan , Amir Haqshenas , Samuel Hetterich

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…

Discrete Mathematics · Computer Science 2019-05-03 Tobias Friedrich , Anton Krohmer , Ralf Rothenberger , Thomas Sauerwald , Andrew M. Sutton

We demonstrate a direct mapping of max k-SAT problems (and weighted max k-SAT) to a Chimera graph, which is the non-planar hardware graph of the devices built by D-Wave Systems Inc. We further show that this mapping can be used to map a…

The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…

Quantum Physics · Physics 2020-06-08 Madita Willsch , Dennis Willsch , Fengping Jin , Hans De Raedt , Kristel Michielsen

Quantum computing is rapidly advancing, harnessing the power of qubits' superposition and entanglement for computational advantages over classical systems. However, scalability poses a primary challenge for these machines. By implementing a…