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Second International Meeting for Applied Geoscience & Energy

Quantum computing in geophysics: Algorithms, computational costs, and future applications

Shahpoor Moradi, Daniel O. Trad, K. A. Innanen

Published Aug 27, 2018• 12 citations
Publisher

Abstract

Accurate modeling of seismic wave propagation in the subsurface of the earth is essential for understanding earthquake dynamics, characterizing seismic hazards on global scales and hydrocarbon reservoir exploration and monitoring on local scales. These are among the most challenging computational problems in geoscience. Despite algorithmic advances and the increasingly powerful computational resources currently available, including fast CPUs, GPUs and large volumes of computer memory, there are still daunting computational challenges in simulating 3D seismic wave propagation in complex earth environments. Recent advances in quantum computing are suggestive that geoscience may soon begin to benefit from this promising field. For example, Finite Difference (FD) modeling is the most widely used method to simulate seismic wave propagation. In the frequency domain, FD methods reduce solutions of the wave equation into systems of linear equations; such systems are just the type that quantum algorithms may be capable of solving with exponential speedup, in comparison with classical algorithms. For the computational geophysicist, to prepare to take advantage of these speed-ups, which could arrive in as few as 5-10 years, the tasks at hand are (1) to become familiar with the logic and concepts associated with quantum computing, and (2) to map our key computational algorithms (e.g., frequency domain FD) to this domain. Presentation Date: Monday, October 15, 2018 Start Time: 1:50:00 PM Location: 204B (Anaheim Convention Center) Presentation Type: Oral

DOI
10.1190/segam2018-2998507.1

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Accurate modeling of seismic wave propagation in the subsurface of the earth is essential for understanding earthquake dynamics, characterizing seismic hazards on global scales and hydrocarbon reservoir exploration and monitoring on local scales. These are among the most challenging computational problems in geoscience. Despite algorithmic advances and the increasingly powerful computational resources currently available, including fast CPUs, GPUs and large volumes of computer memory, there are still daunting computational challenges in simulating 3D seismic wave propagation in complex earth environments. Recent advances in quantum computing are suggestive that geoscience may soon begin to benefit from this promising field. For example, Finite Difference (FD) modeling is the most widely used method to simulate seismic wave propagation. In the frequency domain, FD methods reduce solutions of the wave equation into systems of linear equations; such systems are just the type that quantum algorithms may be capable of solving with exponential speedup, in comparison with classical algorithms. For the computational geophysicist, to prepare to take advantage of these speed-ups, which could arrive in as few as 5-10 years, the tasks at hand are (1) to become familiar with the logic and concepts associated with quantum computing, and (2) to map our key computational algorithms (e.g., frequency domain FD) to this domain. Presentation Date: Monday, October 15, 2018 Start Time: 1:50:00 PM Location: 204B (Anaheim Convention Center) Presentation Type: Oral
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
Abstract Mathematical and computational challenges involved in seismic data processing presents an opportunity for early adoption of quantum computation methods for end-to-end seismic data processing. Existing methods of seismic data processing involve processes with exponential complexities that result in approximations as well as conversion of some of the continuous phenomena into a stochastic one. In the classical computation methods, the mentioned approximations and assumptions enable us to obtain acceptable results in commercially viable time. This paper proposes alternatives of the classical computations that exist in the quantum computation ecosystem along with the computational advantages it holds. The paper also presents potential contributions of the petroleum industry towards sustaining the quantum computation technologies. Fundamentally seismic data processing involves solutions for systems of linear equations and its derivatives. Quantum computation ecosystem holds efficient solutions for systems of linear equations. In the frequency domain, Finite-Difference modelling reduces seismic-wave equations to systems of linear equations. In the classical computational setup the seismic acquisition involves treatment of the recorded waves as rays and has limited summation provision for recreating the natural reflection or refraction phenomena that is continuous instead of being a stochastic process. The algorithms in the quantum ecosystem allow us to consider summation of signals from all possible paths between the source and the receiver, by amplitude-probability. In addition to the systems of linear equations and their solution with corresponding methods in the quantum ecosystem the fourier transformation and partial differential equations enable us to decompose the waves and apply the physics equation to obtain the desired objective. Quantum-algorithms facilitate exponential speed-up in seismic data processing. The PDE-constrained optimization inverts subsurface P-wave velocity. While going through the seismic data processing steps it is found that the fourier transformation algorithms are derived as a decomposition of the diagonal matrix. The key difference between the fast fourier transform and the quantum fourier transform is that the quantum fourier transformation is used as the building block of several quantum algorithms. Seismic inversion involves laws of physics and calculation that are guided by the ordinary differential equations. In the quantum computation ecosystem these algorithms for linear ordinary differential equations for linear partial differential equations have the complexity of (1/e), where ‘e’ is the tolerance. The insights brought by successful implementation of end-to-end seismic data processing with algorithms in the quantum computation domain enables us to drill most optimally located wells and hence facilitate cost saving. Even with a reduction of 10% in the total number of wells that we drill, we can possibly fund development of one quantum computer hence ensuring economic sustainability of the technology. The novelty of the presented paper lies in the comparative analysis of the classical methods with its counterparts in the quantum ecosystem. It explains the technological and economical aspects of the technology such that extensive knowledge of quantum technology is not compulsory for grasping its contents.
The computational demands of geoscientific workflows are rapidly increasing in both complexity and scale, pushing the limits of classical computing. Quantum computing has emerged as a promising paradigm to address some of these challenges. This paper surveys the growing intersection between quantum computing and energy geosciences, highlighting recent developments and initiatives. To illustrate the practical relevance of this emerging field, we present a case study on seismic traveltime inversion using a variational quantum circuit. In this example, a hybrid quantum-classical workflow is used to reconstruct velocity models from noisy traveltime data, demonstrating how quantum circuits can solve geophysical inverse problems. While modest in scale, the study offers insights into the formulation and implementation of quantumassisted inversion. As quantum hardware advances and algorithmic frameworks mature, quantum computing is poised to become a transformative tool in the computational landscape of energy geosciences.
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.
Abstract ABSTRACT Quantum computing harnesses the principles of quantum mechanics to solve problems that are intractable for classical computers. Quantum annealing, a specialized approach within quantum computing, is particularly effective for optimization tasks, as it leverages quantum tunneling to escape local minima and efficiently explore complex energy landscapes. In geosciences, many problems are framed as high-dimensional optimization problems, including seismic inversion, which aims to estimate subsurface impedances from seismic data for accurate geological interpretation and resource exploration. A novel application of quantum computing for seismic inversion is presented, marking the first instance of inverting seismic data to estimate both P-wave and S-wave impedances using a quantum annealer. Building upon the prior work, which demonstrated the estimation of acoustic impedances from post-stack data using a two-step framework, we propose an enhanced workflow capable of inverting both post-stack and pre-stack seismic data in a single step. This advancement significantly reduces the number of qubits per model parameter (from 20 to 5) while improving computational speed (from 20 seconds to 6.3 seconds). The seismic inversion is implemented using the D-Wave Leap hybrid solver, achieving impedance estimation within 4-9 seconds, with the quantum processing unit (QPU) contributing just 0.043-0.085 seconds. Comparative analysis with simulated annealing reveals that quantum annealing produces impedance models closely matching true values in a single epoch, whereas simulated annealing requires 10 epochs for improved accuracy. These findings underscore the transformative potential of quantum computing for real-time, high-precision seismic inversion, marking a crucial step toward fully quantum-driven geophysical solutions.