# Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

@article{Glover2019QuantumBA, title={Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models}, author={Fred W. Glover and Gary A. Kochenberger and Yu Du}, journal={Ann. Oper. Res.}, year={2019}, volume={314}, pages={141-183} }

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…

## 142 Citations

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

- Computer Science4OR
- 2020

It is shown 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.

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.

Machine learning framework for quantum sampling of highly constrained, continuous optimization problems

- Computer ScienceApplied Physics Reviews
- 2021

This work developed a generic, machine learning-based framework for mapping continuous-space inverse design problems into surrogate quadratic unconstrained binary optimization (QUBO) problems by employing a binary variational autoencoder and a factorization machine.

Quantum Annealing Formulation for Binary Neural Networks

- Computer Science2021 Digital Image Computing: Techniques and Applications (DICTA)
- 2021

This work devise a quadratic unconstrained binary optimization formulation for the training problem of binary neural networks, and shows how the problem can be optimized directly on a quantum annealer, thereby opening up to the potential gains of quantum computing.

Domain-Specific Quantum Architecture Optimization

- Computer Science
- 2022

This paper provides performance guarantees by integrating architecture optimization with an optimal compiler, evaluates the impact of connectivity customization under a realistic crosstalk error model, and benchmarks on realistic circuits of near-term interest, such as the quantum approximate optimization algorithm (QAOA) and quantum convolutional neural network (QCNN).

Calculating Nash Equilibrium on Quantum Annealers

- Computer Science
- 2021

It is shown that adding penalty terms to the quadratic function formulation of Nash equilibrium gives a quadRatic unconstrained binary optimization (QUBO) formulation of this problem that can be executed on quantum annealers.

Characterization of QUBO Reformulations for the Maximum k-Colorable Subgraph Problem

- Physics
- 2020

Both adiabatic quantum computers, and algorithms for gate-based quantum computers are able to address the solution of quadratic unconstrained binary optimization (QUBO) problems. This allows the use…

Applying the Hubbard-Stratonovich Transformation to Solve Scheduling Problems Under Inequality Constraints With Quantum Annealing

- Computer ScienceFrontiers in Physics
- 2021

The implementation of the Hubbard-Stratonovich transformation carried out in this paper on a scheduling use case suggests that this approach could be investigated further and applied to a variety of real-life integer programming problems under multiple constraints to lower the cost of mapping to QUBO, a key step towards the near-term practical application of quantum computing.

The Useful Quantum Computing Techniques for Artificial Intelligence Engineers

- Computer Science2020 International Conference on Information Networking (ICOIN)
- 2020

Some useful quantum computing techniques for AI engineers such as Quadratic Unconstrained Binary Optimization (QUBO), Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), and Harrow-Hassidim-Lloyd (HHL) algorithm are introduced.

When to Build Quantum Software?

- Computer ScienceArXiv
- 2021

Design of an interactive advisor is presented, which augments users while deciding to invest into quantum software development as a plausible future option in their application context and business process modeling and natural language similarity analysis are applied to associated business context with computational problems.

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