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.
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.
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
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.
Quantum computing is increasingly recognized as a transformative technology in geophysics, offering the potential to significantly enhance computational power and efficiency. This advancement holds promise for the simulation and processing of complex geological data at unprecedented speeds. Recent studies have begun exploring the application of quantum computing methods to simplified versions of seismic inversion problems, underscoring the technology’s capability to address real-world inverse problems. The primary aim of this study is to tackle a realistic, scalable, and business-relevant problem by estimating acoustic impedances from seismic trace data using a quantum computer. To the best of our knowledge, this is the first instance of seismic impedances being predicted from seismic data through quantum computing, with a discussion on the advantages of solving the inverse problem on quantum processing units (QPUs). In this paper, we leverage the D-Wave quantum annealer to tackle the poststack seismic inversion problem, employing a novel two-step workflow. In the first step, we utilize the quantum annealer to estimate reflectivities from seismic data. Subsequently, these estimated normal-incidence reflectivities serve as the basis for predicting acoustic impedances with the same quantum technology. To validate the effectiveness of our approach, we present five examples, juxtaposing the impedance predictions from the D-Wave quantum annealer against those obtained through Simulated Annealing—a stochastic global optimizer traditionally employed for seismic inversion. Remarkably, the impedances derived from the quantum annealer matched closely with the true values in just a single epoch, whereas simulated annealing required 10 epochs to achieve a similar accuracy. Furthermore, the QPUs within our hybrid solver took only about 0.08 seconds to estimate these seismic impedances. This is remarkably efficient when compared to the time needed by both the classical component of the hybrid solver and simulated annealing, which each took over 10 seconds. This highlights the potential of QPUs to entirely resolve the seismic inverse problem in under a second, underscoring the transformative impact that quantum computing can have in the field of geophysics.
Due to the increasing volume and complexity of seismic datasets, seismic processing is confronted with increasing computational demands, which necessitate the implementation of innovative solutions such as quantum computing. This study applies the Quantum Fourier Transform (QFT), implemented via the Qiskit framework, to two geophysical applications: computing instantaneous seismic attributes and performing Multi-Dimensional Convolution (MDC). We present a workflow for preparing seismic data for QFT processing, demonstrating results with accuracy comparable to conventional Fourier Transform (FT)-based methods. Although executed on a quantum simulator, the approach is compatible with quantum hardware, promising significant performance gains through qubit superposition. This work offers a new framework for integrating quantum algorithms into geophysical processing workflows, highlighting their potential to improve efficiency and scalability as quantum technology advances.
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 algorithms offer new avenues for solving partial differential equations (PDEs). While the potential for end-to-end quantum advantage is at present not well understood, recent literature presents explicit circuit constructions for solving certain classes of linear PDEs in the frequency domain and thus offers concrete examples to study. In this work, we develop end-to-end implementations of these quantum circuits compiled to machine-level instructions and benchmark them in both numerical simulations and IBMQ hardware experiments. We focus on the advection, wave, and Poisson equations and study quantum circuits that propagate the dynamics in frequency space via the quantum Fourier transform using approximate methods based on a first-order approximation which offer compact representations with uncontrollable approximation error, and polynomial approximation methods based on quantum signal processing (QSP) leading to deeper circuits with tunable algorithmic error. In addition, we experimentally demonstrate that the QSP-augmented algorithm can provide accurate solutions under realistic hardware constraints. Finally, we extend our method to address non-homogeneous Dirichlet boundary conditions and verify it numerically for a Poisson equation with source term obtained from high-fidelity physics simulations of a capacitively coupled plasma.