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The Potential of Quantum Computing for Geoscience

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Abstract

Characterization and modeling of geomedia, computing their effective flow, transport, elastic, and other properties, and simulating various phenomena that occur there constitute some of the most intensive calculations in science and engineering. Over the past twenty five years, however, development of quantum computers has made great progress, and powerful quantum algorithms have been developed for simulating many important and computationally difficult problems, with the potential for enormous speed-up over the most efficient classical algorithms. This perspective describes such algorithms and discusses their potential applications to problems in geoscience, ranging from reconstruction and modeling of geomedia, to simulating fluid flow by the Stokes and Navier-Stokes equations, or lattice Boltzmann and lattice gas methods, numerical solution of the advection-diffusion equation, pattern recognition in and analysis of big data, machine learning methods, and image processing. Although several hurdles remain that must be overcome before practical computations with quantum computers, and in particular those associated with geoscience, become possible, such as designing fault-tolerant quantum computers, which is still far into the future, noisy intermediate-scale computers are already available whose capabilities have been demonstrated for various problems.

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Notes

  1. When a group of particles, or more generally, elements interact, or share spatial proximity such that the quantum state of each of them cannot be described independently of those of the others, including when they are separated by large distances, one has quantum entanglement.

  2. The Hilbert space generalizes the methods of linear algebra and calculus from finite-dimensional Euclidean vector space to those that may be infinite-dimensional ones. It is a vector space with an inner product that defines a distance function for which it is a complete metric space.

  3. Recall that in quantum mechanics, particles, such as electrons, are described by a wave function. As long as there exists a definite phase relation between different states, the system is said to be coherent. Such a phase relationship is necessary to carry out quantum computing on quantum information encoded in quantum states, with coherence preserved under the laws of quantum physics.

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  1. Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA, 90089-1211, USA

    Muhammad Sahimi

  2. Colorado School of Mines, Golden, CO, 80401, USA

    Pejman Tahmasebi

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Sahimi, M., Tahmasebi, P. The Potential of Quantum Computing for Geoscience. Transp Porous Med 145, 367–387 (2022). https://doi.org/10.1007/s11242-022-01855-8

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