Lecture: Quantum Annealing

Van Dung Nguyen, Ling Wu, F. Remacle +1 more

Kristel F. L. Michielsen

Madita Willsch, Dennis Willsch, Kristel F. L. Michielsen

Quantum computing is a new emerging computer technology. Current quantum computing devices are at a development stage where they are gradually becoming suitable for small real-world applications. This lecture is devoted to the practical aspects of programming such quantum computing devices. The first part of these lecture notes focuses on programming gate-based quantum computers, and the second part shows how to program quantum annealers.

Eliahu Cohen, Boaz Tamir

Kevin Tole, Edward Fondo, Fullgence Mwachoo Mwakondo

University timetabling is a classical NP-Hard combinatorial constraint problem that involves scheduling of courses, lecturers, students, classrooms, and timeslots while satisfying a set of constraints, with the main goal of minimizing conflicts. To solve this problem, we propose a novel Quantum Annealing and Topological Data Analysis (QA–TDA) algorithm that starts with an initial feasible solution, followed by iterative refinement using Quantum annealing configurations. TDA analyses the optimization landscape through persistent homology by detecting promising regions of interest in the solution space, which are clustered and subjected to quantum re-annealing using customized Hamiltonians-adaptive annealing schedules. QA-TDA model achieves a balance between global exploration and local exploitation, which improves convergence efficiency and solution robustness. Experimental results demonstrate that our hybrid model consistently outperforms baseline models across all evaluation metrics. In particularly on the most complex dataset, QA– TDA achieved a Conflict-Free Rate (CFR) of 94.3%. Additionally, an ablation study was conducted to validate the contribution of each component of the proposed model. Furthermore, clustering and K-Nearest Neighbour (K-NN) analyses confirm the robustness and consistency of the proposed approach across datasets of varying sizes and complexity. These findings highlight the great performance, scalability, and reliability of the integrated QA–TDA model for real-world academic scheduling applications.

Xavier Waintal, Chen-How Huang, Christoph W. Groth

This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the "quantics" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the "quantics" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.