Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange

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

doi:10.1007/s10479-022-04695-3

Cited by 12 publications

(2 citation statements)

References 28 publications

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“…that can be converted to the classical QUBO model -Quadratic Unrestricted Binary Optimization, which then maps over onto the quantum Ising model [110][111][112] . In the final cost function, the Ising Hamiltonian, the constants (external field and spin interactions) are then determined by the constraint matrix {a f r } (Eq.…”

Section: Qaoa Basicsmentioning

confidence: 99%

Quantum information processing with superconducting circuits: a perspective

Wendin¹

2023

Preprint

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The last five years have seen a dramatic evolution of platforms for quantum computing, taking the field from physics experiments to quantum hardware and software engineering. Nevertheless, despite this progress of quantum processors, the field is still in the noisy intermediate-scale quantum (NISQ) regime, seriously limiting the performance of software applications. Key issues involve how to achieve quantum advantage in useful applications for quantum optimization and materials science, connected to the concept of quantum supremacy first demonstrated by Google in 2019. In this article we will describe recent work to establish relevant benchmarks for quantum supremacy and quantum advantage, present recent work on applications of variational quantum algorithms for optimization and electronic structure determination, discuss how to achieve practical quantum advantage, and finally outline current work and ideas about how to scale up to competitive quantum systems.

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Section: Qaoa Basicsmentioning

confidence: 99%

Quantum information processing with superconducting circuits: a perspective

Wendin¹

2023

Preprint

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“…Still, such an approach increments the number of qubits and connections needed to solve these problems. We remark that an alternative approach to handle inequality constraints with penalization would be to develop direct algorithms that respect the constraints by construction, as illustrated in [33] for the asset exchange problem.…”

Section: Introductionmentioning

confidence: 99%

Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Montañez-Barrera,

Willsch,

Maldonado-Romo

et al. 2024

Quantum Sci. Technol.

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Solving combinatorial optimization problems of the kind that can be codiﬁed by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.

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Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange

Glover

Kochenberger

Ma³

et al. 2022

Ann Oper Res

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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) 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 important instance of these models called the Asset Exchange Problem (AEP). Solutions to the AEP enable market players to identify exchanges of assets that benefit all participants. Such exchanges are generated by a combination of two optimization technologies for this class of QUBO-Plus models, one grounded in network optimization and one based on a new metaheuristic optimization approach called combinatorial chaining. This combination opens the door to expanding the links to quantum computing applications established by QUBO models through the Quantum Bridge Analytics perspective. We show how the modeling and solution capability for the AEP instance of QUBO-Plus models provides a framework for solving a broad range of problems arising in financial, industrial, scientific, and social settings.

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Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange

Cited by 12 publications

References 28 publications

Quantum information processing with superconducting circuits: a perspective

Quantum information processing with superconducting circuits: a perspective

Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange

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