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arXiv:1911.03036

Quantum Bridge Analytics II: Network Optimization and Combinatorial Chaining for Asset Exchange

Fred Glover, Gary A. Kochenberger, Moses Ma, Yu Du

Published Jan 1, 2019• 0 citations
arXivHTMLPDF

Abstract

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications. Part I focused on the Quadratic Unconstrained Binary Optimization (QUBO) model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. Part II (the present paper) examines an application that augments the use of QUBO models, by disclosing a context for coordinating QUBO solutions through a model we call the Asset Exchange Problem (AEP). Solutions to the AEP enable individuals or institutions to take fuller advantage of solutions to their QUBO models by exchanges of assets that benefit all participants. Such exchanges are generated by a combination of two optimization technologies, one grounded in network optimization and one based on a new metaheuristic optimization approach called combinatorial chaining. This combination provides a flexibility to solve AEP variants that open the door to additional links to quantum computing applications and additional applications via the Quantum Bridge Analytics perspective. We show how this modeling and solution capability gives rise to an Asset Exchange Technology that embraces a broad range of financial, industrial, scientific and social settings. Examples are presented that show the nature of these processes from a tutorial perspective.

DOI
10.13140/rg.2.2.33981.00480

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Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications. Part I focused on the Quadratic Unconstrained Binary Optimization (QUBO) model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. Part II (the present paper) examines an application that augments the use of QUBO models, by disclosing a context for coordinating QUBO solutions through a model we call the Asset Exchange Problem (AEP). Solutions to the AEP enable individuals or institutions to take fuller advantage of solutions to their QUBO models by exchanges of assets that benefit all participants. Such exchanges are generated by a combination of two optimization technologies, one grounded in network optimization and one based on a new metaheuristic optimization approach called combinatorial chaining. This combination provides a flexibility to solve AEP variants that open the door to additional links to quantum computing applications and additional applications via the Quantum Bridge Analytics perspective. We show how this modeling and solution capability gives rise to an Asset Exchange Technology that embraces a broad range of financial, industrial, scientific and social settings. Examples are presented that show the nature of these processes from a tutorial perspective.
Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications. Part I focused on the Quadratic Unconstrained Binary Optimization (QUBO) model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. Part II (the present paper) examines an application that augments the use of QUBO models, by disclosing a context for coordinating QUBO solutions through a model we call the Asset Exchange Problem (AEP). Solutions to the AEP enable individuals or institutions to take fuller advantage of solutions to their QUBO models by exchanges of assets that benefit all participants. Such exchanges are generated by an approach called combinatorial chaining, which provides a flexibility to solve AEP variants that open the door to additional links to quantum computing applications. Examples are presented that show the nature of these processes from a tutorial perspective.
Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications. Part I focused on the Quadratic Unconstrained Binary Optimization (QUBO) model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. Part II (the present paper) introduces the domain of QUBO-Plus models that enables a larger range of problems to be handled effectively. After illustrating the scope of these QUBO-Plus models with examples, we give special attention to an importance instance of these models called the Asset Exchange Problem (AEP).
The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies. This tutorial discloses the basic features of the QUBO model that give it the power and flexibility to encompass the range of applications that have thrust it onto center stage of the optimization field. We show how many different types of constraining relationships arising in practice can be embodied within the "unconstrained" QUBO formulation in a very natural manner using penalty functions, yielding exact model representations in contrast to the approximate representations produced by customary uses of penalty functions. Each step of generating such models is illustrated in detail by simple numerical examples, to highlight the convenience of using QUBO models in numerous settings. We also describe recent innovations for solving QUBO models that offer a fertile avenue for integrating classical and quantum computing and for applying these models in machine learning.
The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of these new devices. These problems are recurrent in industrial applications and they are in general difficult for classical computing hardware. In this work, we provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. We focus mainly on four different approaches including digitizing the adiabatic quantum computing, global quantum optimization algorithms, the quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. We also discuss the quantum algorithms that are custom designed to solve certain types of QUBO problems.