# Finding Maximum Cliques on the D-Wave Quantum Annealer

@article{Chapuis2019FindingMC, title={Finding Maximum Cliques on the D-Wave Quantum Annealer}, author={Guillaume Chapuis and Hristo N. Djidjev and Georg Hahn and Guillaume Rizk}, journal={Journal of Signal Processing Systems}, year={2019}, volume={91}, pages={363-377} }

This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. [... ] Key Method For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms… Expand

## 47 Citations

### Solving Large Maximum Clique Problems on a Quantum Annealer

- Computer ScienceQTOP@NetSys
- 2017

This article investigates methods for decomposing larger problem instances into smaller ones, which can subsequently be solved on D-Wave, and prune as many generated subproblems that don’t contribute to the solution as possible in order to reduce the computational complexity.

### Decomposition Algorithms for Solving NP-hard Problems on a Quantum Annealer

- Computer ScienceJ. Signal Process. Syst.
- 2021

A general framework for a decomposition algorithm for NP-hard graph problems aiming to identify an optimal set of vertices is studied and several pruning and reduction techniques are proposed to speed up the recursive decomposition.

### Advanced unembedding techniques for quantum annealers

- Computer Science2020 International Conference on Rebooting Computing (ICRC)
- 2020

This work presents tailored unembedding techniques for four important NP-hard problems: the Maximum Clique, Maximum Cut, Minimum Vertex Cover, and Graph Partitioning problems, and demonstrates that the proposed algorithms outperform the currently available ones in that they yield solutions of better quality, while being computationally equally efficient.

### Parallel quantum annealing

- PhysicsScientific reports
- 2022

This work proposes a novel method, called parallel quantum annealer, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum anNealer, assuming enough physical qubits are available to embed more than one problem.

### Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer

- Computer ScienceArXiv
- 2022

A new kernel that quantifies success for the task of computing a coreperiphery partition for an undirected network is proposed and a sparsified version of the original QUBO is developed which increases the available problem dimension for the quantum annealer.

### Reducing quantum annealing biases for solving the graph partitioning problem

- Computer ScienceCF
- 2021

This work quantifies the bias of the implementation of the constraint on the quantum annealer and proposes an iterative method to correct any biases, and applies this concept to Graph Partitioning, an important NP-hard problem, which asks to find a partition of the vertices of a graph that is balanced and minimizes the cut size.

### Core-periphery Partitioning and Quantum Annealing

- Computer ScienceKDD
- 2022

A new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network is proposed and a sparsified version of the original QUBO is developed which increases the available problem dimension for the quantum annealer.

### Finding the chromatic sums of graphs using a D-Wave quantum computer

- Computer ScienceThe Journal of Supercomputing
- 2019

Starting from a BIP (binary integer programming) formulation, a QUBO (quadratic unconstrained binary optimization) formulation of the chromatic sum problem is developed, which is acceptable to a D-Wave quantum computer.

### Using Machine Learning for Quantum Annealing Accuracy Prediction

- Computer ScienceAlgorithms
- 2021

This work focuses on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry, and trains a machine learning regression model that predicts the clique size found by D-Wave.

### Optimizing the optimizer: decomposition techniques for quantum annealing

- Computer ScienceQuantum Mach. Intell.
- 2021

The results indicate that the Qbsolv algorithm is, at this time, the state-of-the-art in producing quality solutions, in a timely fashion, to a variety of theoretical and real-world problems too large to directly embed onto a quantum annealing device.

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