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arXiv:quant-ph/0211152 · Springer eBooks

Scalable Architecture for Adiabatic Quantum Computing of Np-Hard Problems

William M. Kaminsky, Seth Lloyd

Published Jan 1, 2004• 58 citations
arXivHTMLPDF
DOI
10.1007/978-1-4419-9092-1_25

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We introduce a framework for mapping NP-Hard problems to adiabatic quantum computing (AQC) architectures that are heavily restricted in both connectivity and dynamic range of couplings, for which minor-embedding -- the standard problem mapping method -- cannot be directly applied. Separating the mapping into two distinct stages, we introduce problem-specific reductions for both quadratic unconstrained binary optimisation (QUBO) and satisfiability (SAT) and develop the subdivision-embedding method that is suitable for directly embedding onto these heavily restricted architectures. The theory underpinning this framework provides tools to aid in the manipulation of Ising Hamiltonians for the purposes of Ising energy minimisation, and could be used to assist in developing and optimising further problem mapping techniques. For each of the problem mapping methods presented, we examine how the physical qubit count scales with problem size on architectures of varying connectivity.
QUBO problems are NP-hard and have wide applications in optimization, including finance, logistics, machine learning, and combinatorial problems. However, classical algorithms employed for solving them can often get stuck in local minima. This paper presents an Adiabatic Quantum Computing (AQC) approach towards finding an optimal solution for QUBO problems. The QUBO problem has been first encoded into Hamiltonians. The adiabatic theorem has been used to achieve success of an AQC solution with a rate which is found to be dependent on relative gap between the ground state and first exited state of the Hamiltonian.