Summary Quantum computing could be a potential game-changer in industry sectors relying on the efficient solutions of large-scale global optimization problems. Exploration geoscience, is full of optimization problems and hence is a good candidate for application of quantum computing. It was recently suggested that quantum annealing, a form of adiabatic quantum computer, is a much better suited quantum computing platform for optimization problems than gate-based quantum computing. In this work, we show how the residual statics estimation problem can be solved on the quantum annealer and present our first results obtained on a quantum computer.
Summary Quantum computing could be a potential game-changer in industry sectors relying on the efficient solutions of large-scale global optimization problems. Exploration geoscience, is full of optimization problems and hence is a good candidate for application of quantum computing. It was recently suggested that quantum annealing, a form of adiabatic quantum computer, is a much better suited quantum computing platform for optimization problems than gate-based quantum computing. In this work, we show how the residual statics estimation problem can be solved on the quantum annealer and present our first results obtained on a quantum computer.
Summary Quantum annealing emerged as a very promising tool for solving combinatorial optimization problems. In particular, residual refraction statics estimation has been identified to be the first potential industrial use case of quantum annealing in geoscience. The currently available quantum annealers have still too small computing capabilities to effectively and independently estimate residual statics on problems of industrial scale. On the other hand, a quantum annealer-assisted hybrid solver, combining classical and quantum information processing could already be a viable tool for this purpose. Here we show the application of such a hybrid solver to the residual refraction statics estimation through stack-power maximization on a significant subset of the SEAM Arid model dataset, comprising of over two thousand gathers. We benchmark our approach against a dedicated deterministic classical solver, showing that in a fixed amount of time per gather, the quantum annealer-assisted solution can in many instances outperform the standard approach.
ABSTRACT Much of recent progress in geophysics can be attributed to the adaptation of heterogeneous high-performance computing architectures. It is projected that the next major leap in many areas of science, and hence hopefully in geophysics too, will be due to the emergence of quantum computers. Finding a right combination of hardware, algorithms, and a use case, however, proves to be a very challenging task — especially when looking for a relevant application that scales efficiently on a quantum computer and is difficult to solve using classical means. We find that maximizing stack power for residual statics correction, an NP-hard combinatorial optimization problem, appears to naturally fit a particular type of quantum computing known as quantum annealing. We express the underlying objective function as a quadratic unconstrained binary optimization, which is a quantum-native formulation of the problem. We choose some solution space and define a proper encoding to translate the problem variables into qubit states. We find that these choices can have a significant impact on the maximum problem size that can fit on the quantum annealer and on the fidelity of the final result. To improve the latter, we embed the quantum optimization step in a hybrid classical-quantum workflow, which aims to increase the frequency of finding the global, rather than some local, optimum of the objective function. Finally, we find that a generic, black-box, hybrid classical-quantum solver also could be used to solve stack-power maximization problems proximal to industrial relevance and capable of surpassing deterministic solvers prone to cycle skipping. A custom-built workflow capable of solving larger problems with an even higher robustness and greater control of the user appears to be within reach in the very near future.
Summary Recent progress in geophysics can be attributed to developments in heterogeneous HPC architectures, with one of the next major leaps being forecasted to be due to quantum computers. It is, however, very difficult to find the right combination of hardware, algorithms and a use-case. This is especially true for applications which have to be simultaneously: relevant and operating at scales where problems become difficult to solve using classical means. Maximizing stack-power for improved near surface characterization and velocity model building, an NP-hard combinatorial optimization problem, appears to naturally fit a particular type of quantum computing known as quantum annealing. We present the quantum-native formulation of this problem. Furthermore, in order to improve the probability of success we embed it in a hybrid classical-quantum workflow. We present the results on controlled experiments run using a 5000-qubit machine and discuss the impact of different classical to quantum problem re-formulations.
Abstract In an era of customized hardware designed to tackle specific geophysical challenges, recent advancements in quantum computing could offer promising solutions to complex global optimization problems using hybrid quantum-classical solvers. We introduce an application of seismic data processing where the stack power of the traces is maximized through quantum annealing for surface-consistent phase and amplitude refraction residual calculations. Refraction residual corrections are a necessary step in the processing workflow to obtain a detailed characterization of the subsurface. The problem of estimating accurate refraction residuals can be solved in a framework where relative time shifts and amplitude distortions of seismic traces are evaluated in multiple common-midpoint-offset bins through computerized cross-correlation operations. The results are then used to build a system of linear equations that is simultaneously inverted for surface-consistent shot and receiver phase and amplitude variations. We rewrote the problem by substituting the cross-correlation operations with global optimization performed by a “black-box” hybrid solver, which uses a physical quantum-annealing machine. With the projected hardware and technology improvements of the near future, the new approach is expected to be more accurate than the current solution because it prevents the phenomenon of the so-called cycle skips in the cross-correlation process. The method has been benchmarked with a classical global optimization algorithm and tested with promising results on synthetics of industrial size and relevance. A first attempt of application on field data has also been carried out. Quantum-annealing-based global optimization can be applied to other disciplines such as material science, logistics, and finance.
Quantum computing is a new form of computational technology, which can potentially be used to solve certain problems faster than is possible using classical computers. For this reason, there is an industry drive to develop early quantum computing applications. In this thesis, an overview of quantum computing technologies is provided, along with a practical discussion of the Traveling Salesman Problem, making use of the D-Wave quantum annealer. Subsequently, the main objective of the thesis can be investigated, which is to explore how quantum computing can be used to aid in solving structural optimization problems. Two methods are developed with which simple 2-dimensional truss systems can be optimized using the D-Wave quantum annealer. The methods aim to find the most lightweight choices for the truss cross-sectional areas while complying with material limit stress constraints. The first method directly casts such an optimization problem into a QUBO format. However, due to difficulties with formulating the stress constraint, this method was found to produce a trivial optimization problem. The second method attempts to symbolically solve a truss finite-element problem, using the resulting symbolic expressions to set up an optimization objective function. Although these objective functions are confirmed to work via classical brute-force analysis, the quantum annealer is shown to have difficulty finding the global optimum solution for truss systems with three or more elements. These results indicate that it is not currently beneficial to use quantum annealing for these structural optimization problems. Nevertheless, some improvements to the method for setting up the objective functions are suggested. The next generation of quantum annealers is expected to perform better for these practical applications, potentially becoming a useful tool in the engineering toolbox.
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.