An Application of Quantum Annealing Computing to Seismic Inversion

Souza, Alexandre M.; Cirto, Leonardo J. L.; Martins, Eldues O.; Hollanda, N. Linneu; Roditi, I.; Correia, Maury Duarte; Sá, Nahum; Sarthour, R. S.

doi:10.3389/fphy.2021.748285

Cited by 15 publications

(5 citation statements)

References 60 publications

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“…In general, we modify equation (24) to include free parameters to be adjusted for the different kinds of problems. Therefore, equation ( 24) is rewritten by…”

Section: Unbalanced Penalizationmentioning

confidence: 99%

“…In this context, the parameters are adjusted to minimize the expectation value of the cost Hamiltonian using a classical optimizer. Multiple approaches for solving combinatorial optimization problems using QAOA or QA can be found in the literature, for example, in logistics [22], finance [5,[23][24][25], energy [26], communications [27], automotive industry [28], traffic signaling [29], among others.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In general, we modify equation (24) to include free parameters to be adjusted for the different kinds of problems. Therefore, equation ( 24) is rewritten by…”

Section: Unbalanced Penalizationmentioning

confidence: 99%

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.

View full text Add to dashboard Cite

show abstract

“…However, they fail for matrices with high condition numbers. The first practical application to utilize QA for linear systems was Souza et al, who presented a seismic inversion problem, which they solved in a least-square manner [47]. Schielein et al presented a road map towards QC-assisted TT, describing data loading, storing, image processing, and image reconstruction problems [48].…”

Section: Related Workmentioning

confidence: 99%

Exploring the Limitations of Hybrid Adiabatic Quantum Computing for Emission Tomography Reconstruction

Nau,

Vija,

Gohn

et al. 2023

J. Imaging

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Our study explores the feasibility of quantum computing in emission tomography reconstruction, addressing a noisy ill-conditioned inverse problem. In current clinical practice, this is typically solved by iterative methods minimizing a L2 norm. After reviewing quantum computing principles, we propose the use of a commercially available quantum annealer and employ corresponding hybrid solvers, which combine quantum and classical computing to handle more significant problems. We demonstrate how to frame image reconstruction as a combinatorial optimization problem suited for these quantum annealers and hybrid systems. Using a toy problem, we analyze reconstructions of binary and integer-valued images with respect to their image size and compare them to conventional methods. Additionally, we test our method’s performance under noise and data underdetermination. In summary, our method demonstrates competitive performance with traditional algorithms for binary images up to an image size of 32×32 on the toy problem, even under noisy and underdetermined conditions. However, scalability challenges emerge as image size and pixel bit range increase, restricting hybrid quantum computing as a practical tool for emission tomography reconstruction until significant advancements are made to address this issue.

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“…There are efficient algorithms that could theoretically be used to solve large systems of equations (Harrow et al, 2009;Subaşı et al, 2019), but these efficiencies may be undone by the implementation details needed to use these algorithms for a particular application (Aaronson, 2015). Current work in the geosciences utilizes a more empirical approach-trying different problems and observing the performance (O'Malley, 2018;Sarkar and Levin, 2018;Greer and O'Malley, 2020;Dukalski, 2021;Henderson et al, 2021;Souza et al, 2022;Dukalski et al, 2023). Generally, the performance on current quantum computers lags behind the performance of classical computers using the best algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…It improves upon previous work by enabling the solution of more realistic problems. Our approach enables 2D seismic inverse analysis, whereas previous work focused on a 1D, layered approach (Souza et al, 2022). Past work in hydrology required the use of an unrealistic set of observations (O'Malley, 2018), whereas the approach used here can handle arbitrary, realistic sets of observations.…”

Section: Introductionmentioning

confidence: 99%

Early steps toward practical subsurface computations with quantum computing

Greer,

O'Malley

2023

Front. Comput. Sci.

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Quantum computing exploits quantum mechanics to perform certain computations more efficiently than classical computers. Current quantum computers have performed carefully tailored computational tasks that would be difficult or impossible for even the fastest supercomputers in the world. This “quantum supremacy” result demonstrates that quantum computing is more powerful than classical computing in some computational regimes. At present, it is unknown if any computational problems related to the Earth's subsurface fall within these regimes. Here, we describe an approach to performing seismic inverse analysis that combines a type of quantum computer called a quantum annealer with classical computing. This approach improves upon past work on applying quantum computing to the subsurface (via subsurface hydrology) in two ways. First, the seismic inverse problem enables better performance from the quantum annealer because of the Earth's relatively narrow distribution of P-wave velocities compared to the broad distribution of hydraulic conductivities. Second, we develop an iterative approach to quantum-computational inverse analysis, which works with a realistic set of observations. By contrast, the previous method used an inverse method that depended on an impractically dense set of observations. In combination, these two advances significantly narrow the gap a quantum-computational advantage for a practical subsurface geoscience problem. Closing the gap completely requires more work, but has the potential to dramatically accelerate inverse analyses for subsurface geoscience.

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An Application of Quantum Annealing Computing to Seismic Inversion

Cited by 15 publications

References 60 publications

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

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

Exploring the Limitations of Hybrid Adiabatic Quantum Computing for Emission Tomography Reconstruction

Early steps toward practical subsurface computations with quantum computing

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