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arXiv:2502.03808 · Geophysics

Pre-stack and post-stack seismic inversion using quantum computing

Divakar Vashisth, Rodney Lessard, Tapan Mukerji

Published Apr 15, 2026• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1190/geo-2025-0186

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Seismic inversion-including post-stack, pre-stack, and full waveform inversion is compute and memory-intensive. Recently, several approaches, including physics-informed machine learning, have been developed to address some of these limitations. Motivated by the potential of quantum computing, we report on our attempt to map one such classical physics-informed algorithm to a quantum framework. The primary goal is to investigate the technical challenges of this mapping, given that quantum algorithms rely on computing principles fundamentally different from those in classical computing. Quantum computers operate using qubits, which exploit superposition and entanglement, offering the potential to solve classically intractable problems. While current quantum hardware is limited, hybrid quantum-classical algorithms-particularly in quantum machine learning (QML)-demonstrate potential for near-term applications and can be readily simulated. We apply QML to subsurface imaging through the development of a hybrid quantum physics-informed neural network (HQ-PINN) for post-stack and pre-stack seismic inversion. The HQ-PINN architecture adopts an encoder-decoder structure: a hybrid quantum neural network encoder estimates P- and S-impedances from seismic data, while the decoder reconstructs seismic responses using geophysical relationships. Training is guided by minimizing the misfit between the input and reconstructed seismic traces. We systematically assess the impact of quantum layer design, differentiation strategies, and simulator backends on inversion performance. We demonstrate the efficacy of our approach through the inversion of both synthetic and the Sleipner field datasets. The HQ-PINN framework consistently yields accurate results, showcasing quantum computing's promise for geosciences and paving the way for future quantum-enhanced geophysical workflows.
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.
This study demonstrates the application of quantum computing based quantum annealing to seismic traveltime inversion, a critical approach for inverting highly accurate velocity models. The seismic inversion problem is first converted into a Quadratic Unconstrained Binary Optimization problem, which the quantum annealer is specifically designed to solve. We then solve the problem via quantum annealing method. The inversion is applied on a synthetic velocity model, presenting a carbon storage scenario at depths of 1000-1300 m. As an application example, we also show the capacity of quantum computing to handle complex, noisy data environments. This work highlights the emerging potential of quantum computing in geophysical applications, providing a foundation for future developments in high-precision seismic imaging.
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
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.