Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing

Abstract

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach on the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.

References in corpus (19)

• Quantum Computing in the NISQ era and beyond
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• Quantum Annealing and Analog Quantum Computation
• Perspectives of quantum annealing: Methods and implementations
• Mathematical Foundation of Quantum Annealing
• Experimental signature of programmable quantum annealing
• Reverse Quantum Annealing Approach to Portfolio Optimization Problems
• Entanglement in a quantum annealing processor
• Scaling advantage in quantum simulation of geometrically frustrated magnets
• A Quantum Annealing Approach for Fault Detection and Diagnosis of Graph-Based Systems
• Simultaneous execution of quantum circuits on current and near-future NISQ systems
• Parallel Quantum Annealing
• Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era
• Solving large Minimum Vertex Cover problems on a quantum annealer
• Decomposition algorithms for solving NP-hard problems on a quantum annealer
• Perils of Embedding for Sampling Problems
• Advanced unembedding techniques for quantum annealers
• Perils of Embedding for Quantum Sampling

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• Quantum annealer accelerates the variational quantum eigensolver in a triple-hybrid algorithm
• Advantages of fixing spins in quantum annealing
• Quantum computing and the stable set problem
• Comparing Quantum Annealing and Spiking Neuromorphic Computing for Sampling Binary Sparse Coding QUBO Problems
• Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking
• Multi-tasking through quantum annealing