Numerical models are essential for investigating and understanding the physics and sound propagation and scattering, given the ocean’s complexity and the limitations of real-world field experiments. High-performance computing has become a primary tool for researchers to simulate long-range sound propagation. Quantum computing is an emerging technique that offers potential speedups over conventional binary computers. However, classical algorithms cannot be directly implemented in quantum systems due to fundamental differences in computing principles. This necessitates the development of quantum ocean acoustic models that remain interpretable within the same context as classical algorithms. This paper presents a quantum formulation for a finite-difference time-domain (FDTD) solver and a parabolic equation (PE) method. The results demonstrate that these quantum algorithms implemented on a simulator reproduce results identical to their classical counterparts, providing a foundation for further developments in quantum-centric ocean acoustics.
Numerical models are essential for investigating and understanding the physics and sound propagation and scattering, given the ocean’s complexity and the limitations of real-world field experiments. High-performance computing has become a primary tool for researchers to simulate long-range sound propagation. Quantum computing is an emerging technique that offers potential speedups over conventional binary computers. However, classical algorithms cannot be directly implemented in quantum systems due to fundamental differences in computing principles. This necessitates the development of quantum ocean acoustic models that remain interpretable within the same context as classical algorithms. This paper presents a quantum formulation for a finite-difference time-domain (FDTD) solver and a parabolic equation (PE) method. The results demonstrate that these quantum algorithms implemented on a simulator reproduce results identical to their classical counterparts, providing a foundation for further developments in quantum-centric ocean acoustics.
SUMMARY Quantum computing has attracted considerable attention in recent years because it promises speedups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers (QCs) are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real QC. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schrödinger equation, which can be simulated directly on a gate-based QC. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real QC IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schrödinger equation by a continuous version allows the replacement of finite differences by other spatial discretization schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, we analyse the computational complexity of the best quantum simulation algorithms for future QCs. This analysis suggests that our quantum computing approach may lead to wavefield simulations that run exponentially faster than simulations on classical computers.
We present a cohesive framework for simulating seismic wave propagation utilizing quantum computing paradigms and their classical tensor network equivalents.
We detail a quantum circuit-based formulation for the explicit finite-difference time-domain (FDTD) solution of the two-dimensional acoustic wave equation and
map this quantum architecture onto a tensor train representation, namely for Matrix Product State (MPS).
The MPS solver enables deterministic simulation of large-scale wavefield dynamics on classical high-performance computing systems.
We demonstrate the MPS representation by computing 2D seismic wavefields on the Marmousi model.
Our results indicate that the MPS representation is a viable direction for computing and scaling wavefield propagation.
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 Physics systems are becoming increasingly complex and require more and more computing time. Quantum computing, which has shown its efficiency on some problems, such as the factorisation of a number with Shor's algorithm, may be the solution to reduce these computation times. Here, the authors propose two quantum numerical schemes for the simulation of physics phenomena, based on the finite difference method. The aim is to see if quantum versions of standard numerical schemes offer an advantage over their classical counterparts, either in accuracy, stability or computation time. First, the authors will present the different phenomena studied as well as the classical solution methods chosen. The authors will then describe the implementation of the quantum numerical schemes and present some results obtained on the different physics phenomena beforehand and then compare both approaches, classical and quantum.
Quantum computing has the potential to solve certain compute-intensive problems faster than classical computing by leveraging the quantum mechanical properties of superposition and entanglement. This capability can be particularly useful for solving Partial Differential Equations (PDEs), which are challenging to solve even for High-Performance Computing (HPC) systems, especially for multidimensional PDEs. This led researchers to investigate the usage of Quantum-Centric High-Performance Computing (QC-HPC) to solve multidimensional PDEs for various applications. However, the current quantum computing-based PDE-solvers, especially those based on Variational Quantum Algorithms (VQAs) suffer from limitations, such as low accuracy, long execution times, and limited scalability. In this work, we propose an innovative algorithm to solve multidimensional PDEs with two variants. The first variant uses Finite Difference Method (FDM), Classical-to-Quantum (C2Q) encoding, and numerical instantiation, whereas the second variant utilizes FDM, C2Q encoding, and Column-by-Column Decomposition (CCD). We evaluated the proposed algorithm using the Poisson equation as a case study and validated it through experiments conducted on noise-free and noisy simulators, as well as hardware emulators and real quantum hardware from IBM. Our results show higher accuracy, improved scalability, and faster execution times in comparison to variational-based PDE-solvers, demonstrating the advantage of our approach for solving multidimensional PDEs.
We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the acoustic wave equation, Maxwell’s equations, and the elastic wave equation. Our formulation is compatible with standard numerical discretization schemes and allows for the efficient implementation of multiple practically relevant time- and space-dependent sources. Furthermore, we demonstrate that subspace energies can be extracted and wave fields compared through an l 2 loss function, achieving optimal precision scaling with the number of samples taken. Additionally, we introduce techniques for incorporating boundary conditions and linear constraints that preserve the anti-Hermitian nature of the equations. Leveraging the Hamiltonian simulation algorithm, our framework achieves a quartic speedup over classical solvers in three-dimensional simulations, under conditions of sufficiently global measurements and compactly supported sources and initial conditions. This quartic speedup is optimal for time-domain solutions, as the Hamiltonian of the discretized wave equations has local couplings. In summary, our framework provides a versatile approach for simulating wave equations on quantum computers, offering substantial speedups over state-of-the-art classical methods.