Abstract
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.
Highlights
Classical computers have had a dramatic impact on hydrology for decades[1,2,3,4,5,6,7,8,9], due largely to the exponential growth in computing power predicted by Moore’s law[10]
We find it appropriate to compare to early work from classical computational hydrology
While quantum computing technology is in an early stage, our intention is to demonstrate that it has progressed to the point where proof-of-principle calculations can be performed for certain subsurface flow problems
Summary
Classical computers have had a dramatic impact on hydrology for decades[1,2,3,4,5,6,7,8,9], due largely to the exponential growth in computing power predicted by Moore’s law[10]. This work can be seen as an early step toward quantum-computational hydrology. Direct methods do not require repeated model runs and are generally less computationally demanding They typically require the hydraulic head to be known throughout the aquifer. Because of their light computational demands, direct methods were commonly used in early computational hydrology[2,15,16] and are still in use today[17]. The approach we take is similar to some early hydrologic inverse analyses (e.g., the work of Hefez et al.2) where inverse problems were formulated as linear and quadratic programs[18]. Programming problems natively, and we use an approach here that formulates a hydrologic inverse problem as a binary quadratic program. The problems solved here with D-Wave’s third generation chip are small by modern standards, but they are larger than the problems solved by Hefez et al.[2] which used a similar methodology and was published between the release of Intel’s third and fourth generation chips
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