This thesis studies several aspects of the quantum annealing (QA) computing approach. Quantum annealers' primary objective is to solve hard computational optimization problems. Because these optimization problems are in the NP-Hard complexity class, they are of great interest in several fields. One of the leading open questions concerning quantum annealers asks whether they will outperform other classical methods for solving these problems; Some aspects of this question are addressed in this thesis. The first part of the thesis investigates whether quantum annealing provides improved performance for solving a particular family of NP problems, called the Quadratic Knapsack Problem (QKP), using the D-Wave Quantum Annealer. The performance metrics used to assess QKP solving are the solution quality and the total runtime, and are benchmarked against other classical solvers. \n \nFurthermore, we extend our research on quantum annealers to propose two use cases for such systems. One is for Blockchain technology, and the second is in the area of quantum chaos. For the first use case of QA, an application for Blockchain's Proof of Work (PoW) is proposed, based on having hard optimization problems as an alternative to PoW hashing challenge, and using quantum annealers as solvers. For the second use case of QA, we propose simulating quantum chaos on the D-Wave Quantum Annealer to study the transition between the deep quantum realm and the classical limit in a chaotic system, and obtain insights into the “quantumness" of quantum annealers.
This thesis studies several aspects of the quantum annealing (QA) computing approach. Quantum annealers' primary objective is to solve hard computational optimization problems. Because these optimization problems are in the NP-Hard complexity class, they are of great interest in several fields. One of the leading open questions concerning quantum annealers asks whether they will outperform other classical methods for solving these problems; Some aspects of this question are addressed in this thesis. The first part of the thesis investigates whether quantum annealing provides improved performance for solving a particular family of NP problems, called the Quadratic Knapsack Problem (QKP), using the D-Wave Quantum Annealer. The performance metrics used to assess QKP solving are the solution quality and the total runtime, and are benchmarked against other classical solvers. \n \nFurthermore, we extend our research on quantum annealers to propose two use cases for such systems. One is for Blockchain technology, and the second is in the area of quantum chaos. For the first use case of QA, an application for Blockchain's Proof of Work (PoW) is proposed, based on having hard optimization problems as an alternative to PoW hashing challenge, and using quantum annealers as solvers. For the second use case of QA, we propose simulating quantum chaos on the D-Wave Quantum Annealer to study the transition between the deep quantum realm and the classical limit in a chaotic system, and obtain insights into the “quantumness" of quantum annealers.
The area of quantum computing is a relatively new and promising branch of computation that hopes to provide help especially in the field of non-deterministic polynomial hard problems. Due to the fact that quantum computers are a heuristically non-binary approach to computation, based on the effects of quantum mechanics, a bunch of advantages and disadvantages come with it. The following work focuses especially on so-called quantum annealers, a special architecture of quantum computers that one can see as an application-specific unit that is using certain quantum mechanical effects to target binary quadratic optimization problems of the class of non-deterministic polynomial-time problems and tries to solve them faster than classical computers can do. Because this is a whole new area, it lacks extensive software support which is addressed in this work. Hence the majority of the thesis aims to develop and extend software that enables users to solve problem instances on a quantum annealer fast and reliable. Furthermore, the necessary steps to solve combinatorial optimization problems are explained and the necessary background of quantum physics theory is given. In conclusion, the main question of this work can be described as follows: 'Is it possible to create an automated pipeline to solve problems on a D-Wave Systems n.d. quantum annealer?'.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
Since the ability of quantum computing to speed up certain, specific computations has a solid theoretical underpinning, it is a natural question to ask if problems in computer vision also benefit from it. This doctoral thesis is in particular concerned with the question if the recently emerging optimization method of quantum annealing is useful for solving combinatorial optimization problems that arise in computer vision. The computer vision problem that is mainly investigated here is the problem of shape matching. The task of shape matching is to obtain the correspondences of two objects in a scene that are described with point clouds. Most often, one is concerned with finding the correspondences for a person who is recorded in 3D two times but with a different pose. The reason why this computer vision problem was picked as an interesting candidate for an application of quantum annealing is because it can be formulated as a difficult combinatorial optimization problem with a quadratic objective. This is close to the type of optimization problem that recent quantum annealing devices try to solve. The biggest difference is that in quantum annealing one a priori has unconstrained problems so that one cannot include equality constraints in the optimization. In the first work of this thesis, multiple methods are presented to overcome this difference and for really small shape matching problems experiments with simulated quantum annealing and with quantum annealing on D-Wave quantum computers were presented. In the second work of this thesis an iterative method was developed so that it was even possible to solve shape matching problems with over 500 vertices. Finally, a third publication looked at problems where one needs to find the correspondences between multiple shapes. Besides applications of quantum annealing for shape matching, this thesis also contains work on solving the motion segmentation problem with quantum annealing and work about integrating a quantum annealer in a neural network to solve computer vision problems. The integration of the quantum annealer in a neural network can also be viewed as the task to learn an appropriate formulation of a computer vision problem in a way that is solvable with a current quantum annealer. Finally, we also present work about an iterative method for compensating limited connectivity in quantum annealing devices. This work has no particular computer vision application in mind, but investigates the performance of the different approaches on Max-Cut problems. The thesis is structured in a cumulative way, so that the individual publications are presented separately. On a broader picture, the works are motivated by the following questions: What could be the impact of quantum annealing on computer vision and how could computer vision algorithms that use quantum annealing look like? And from another perspective: How would the field of computer vision be changed if there were massive advances in building quadratic, unconstrained, binary optimization problem solvers with or even without utilizing quantum computing?
The recent availability of the first commercial quantum computers has provided a promising tool to tackle NP hard problems which can only be solved heuristically with present techniques. However, it is unclear if the current state of quantum computing already provides a quantum advantage over the current state of the art in classical computing. This article assesses the performance of the D-Wave 2X quantum annealer on two NP hard graph problems, in particular clique finding and graph partitioning. For this, we provide formulations as Qubo and Ising Hamiltonians suitable for the quantum annealer and compare a variety of quantum solvers (Sapi, QBSolv, QSage provided by D-Wave Sys, Inc.) to current classical algorithms (METIS, Simulated Annealing, third-party clique finding and graph splitting heuristics) on certain test sets of graphs. We demonstrate that for small graph instances, classical methods still outperform the quantum annealer in terms of computing time, even though the quality of the best solutions obtained is comparable. Nevertheless, due to the limited problem size which can be embedded on the D-Wave 2X chip, the aforementioned finding applies to most of problems of general nature solvable on the quantum annealer. For instances specifically designed to fit the D-Wave 2X architecture, we observe substantial speed-ups in computing time over classical approaches.
This study introduces an innovative application of Parallel Quantum Annealing (PQA) to concurrently solve multiple NP-hard problems on a quantum annealer, leveraging unused qubits on D-Wave's Pegasus architecture to enhance efficiency and accuracy. While parallel execution of different problems on the same quantum annealing device has been previously explored, our application extends the current PQA method, which typically solves a single problem multiple times or different problems with minor embedded combinatorial optimization. This study primarily focuses on three NP-hard problems relevant to integrated circuit design: the Graph Coloring Problem (GCP), the Minimum Vertex Cover Problem (MVCP), and the Graph Partitioning Problem (GPP). After formulating these problems as Quadratic Unconstrained Binary Optimization (QUBO), they were embedded into the D-Wave quantum annealing machine, and the annealing process was run on the combined QUBO. The results were subsequently decoded into individual problems. Our results, quantified via the Time-To-Target (TTT) metric, showcased enhanced efficiency and accuracy in reaching target solutions, indicating a substantial improvement over traditional Quantum Annealing (QA) and Simulated Annealing (SA) methods. The research illustrates the potential of quantum computing for solving complex real-world problems more efficiently and emphasizes the importance of leveraging all available qubits in quantum annealers. The findings can significantly contribute to the development and optimization of quantum computing methods and have broad application implications, particularly in areas where NP-hard problems are prevalent.
In this thesis, we focus on the problem of validating and benchmarking quantum annealers. To this end, we propose two algorithms for solving real-world problems and test how they perform on the current generation of quantum annealers. The first algorithm allows for solving the dynamics of quantum systems (or, in fact, any dynamical systems). The second of the proposed algorithms is suitable for solving a particular family of railway dispatching problems. We assess the performance of those algorithms on the current generation of D-Wave quantum annealers with the assistance of two novel, classical strategies for solving an Ising model also presented in the thesis. The first, tensor network-based approach is a heuristic algorithm tailored for solving instances defined on Chimera-like graphs, thus making it ideal for providing a baseline with which the results from physical annealers can be compared. The other presented approach is a massively parallel implementation of the exhaustive (brute-force) search through the whole solution space. Although the brute-force approach is limited to moderate instance sizes, it has the advantage of being able to compute the low energy spectrum and certify the solutions. Our results suggest that present-day quantum annealers are able to solve a subset of the aforementioned problems. In particular, we show that the D-Wave annealers are capable of capturing the dynamics of a simple quantum system in a specific regime of parameters, and can be used to obtain good-quality solutions for instances of railway conflict management problems. Finally, our findings indicate that the current generation of D-Wave annealers is far from perfect. We discuss problem instances for which the annealers failed to find a good or even feasible solution. We also provide, where possible, a plausible explanation of why some of the presented problems might be hard for the annealers.