Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.
Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.
Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.
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.
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.
In the 1990s, the principles of quantum mechanics were leveraged to describe how discrete combinatorial optimization problems could be solved using a method called quantum annealing. D-Wave Systems, Inc. has since implemented commercial embodiments. We focus on the use of that hardware to solve discrete hydrologic inverse problems, which can become computationally intense at even moderate sizes. In particular, we interrogate whether contemporary quantum annealers with more qubits, lower noise, and reverse annealing features can improve performance. We find modest improvements in speed and accuracy are possible; however, those benefits are currently constrained to a regime of very rapid, approximate solutions on small meshes. As quantum annealers continue to improve, we expect further encroachment on the performance of classical numerical solvers.
Quantum computing has advanced enough that solving basic inverse problems in exploration seismology may be beneficial to show proof-of-concept results. The problems solved should be simple enough to work with the current early state of quantum computing hardware, which would be comparable to problems solved in the early stages of classical computing. We introduce an iterative algorithm for solving PDE-constrained optimization problems on a quantum annealer. We then use this method to invert for subsurface P-wave velocity—using a hybrid of classical and quantum computing—in a simple seismic experiment. Presentation Date: Tuesday, October 13, 2020 Session Start Time: 9:20 AM Presentation Time: 10:10 AM Location: Poster Station 11 Presentation Type: Poster
Accurate modelling of fluid flow in porous media is crucial for applications including hydrology, geological CO₂ storage, hydrogen storage, geothermal energy, and hydrocarbon recovery. The inherent heterogeneity of subsurface formations, characterized by spatial permeability contrasts, fractures, and vugs, leads to large and often ill-conditioned linear systems when discretized at high resolution. Although upscaling techniques reduce computational cost, they may obscure fine-scale features that significantly influence flow behavior, particularly in the presence of small but highly conductive fractures. This study investigates the Variational Quantum Linear Solver (VQLS) as an alternative framework for solving discretized Darcy flow equations in one-, two-, and three-dimensional (1D, 2D, and 3D) homogeneous and heterogeneous systems. VQLS approximates the solution to linear systems of the form Ax = b by preparing a quantum state proportional to the classical solution vector. The framework incorporates a hybrid quantum-classical cost formulation, which strengthens optimization in ill-conditioned systems, and a curvature-aware Adaptive Dynamic Ansatz, which enables principled circuit depth selection without manual tuning. Five experimental modes are evaluated, including fixed-depth training, hybrid cost formulation, adaptive ansatz growth, depth sweep analysis, and hybrid weight sweep. All experiments are conducted using noiseless statevector simulation. The results examine convergence behavior, solution accuracy, and algorithmic limitations in heterogeneous media, providing insight into the practical potential and current constraints of variational quantum solvers for porous media flow modelling.