Abstract. Data assimilation is a crucial component in the Earth science field, enabling the integration of observation data with numerical models. In the context of numerical weather prediction (NWP), data assimilation is particularly vital for improving initial conditions and subsequent predictions. However, the computational demands imposed by conventional approaches, which employ iterative processes to minimize cost functions, pose notable challenges in computational time. The emergence of quantum computing provides promising opportunities to address these computation challenges by harnessing the inherent parallelism and optimization capabilities of quantum annealing machines. In this investigation, we propose a novel approach termed quantum data assimilation, which solves data assimilation problem on quantum annealers. Our data assimilation experiments using the 40-variable Lorenz model were highly promising, showing that the quantum annealers produced analysis with comparable accuracy to conventional data assimilation approaches. In particular, the D-Wave System’s physical quantum annealing machine achieved a great reduction in execution time.
Abstract. Data assimilation is a crucial component in the Earth science field, enabling the integration of observation data with numerical models. In the context of numerical weather prediction (NWP), data assimilation is particularly vital for improving initial conditions and subsequent predictions. However, the computational demands imposed by conventional approaches, which employ iterative processes to minimize cost functions, pose notable challenges in computational time. The emergence of quantum computing provides promising opportunities to address these computation challenges by harnessing the inherent parallelism and optimization capabilities of quantum annealing machines. In this investigation, we propose a novel approach termed quantum data assimilation, which solves data assimilation problem on quantum annealers. Our data assimilation experiments using the 40-variable Lorenz model were highly promising, showing that the quantum annealers produced analysis with comparable accuracy to conventional data assimilation approaches. In particular, the D-Wave System’s physical quantum annealing machine achieved a great reduction in execution time.
Abstract The major computational bottleneck of operational Numerical Weather Prediction (NWP) is data assimilation, in which a high-dimensional, prohibitively expensive variational cost function must be minimised repeatedly, with computational costs scaling alongside model resolution. This work presents a systematic empirical evaluation of an Adaptive Hybrid Variational Quantum-Classical (VQE)-based framework for Four-Dimensional Variational Data Assimilation (4DVAR), benchmarked against Classical BFGS optimisation and three deep learning baselines: a standard Long Short-Term Memory network (LSTM), a task-aligned Data Assimilation LSTM (DA-LSTM), and a Neural Ordinary Differential Equation (Neural ODE) across two canonical chaotic atmospheric models of increasing complexity: the three-variable Lorenz-1963 (L63) and the forty-variable Lorenz-1996 (L96) systems. All experiments were conducted using PennyLane quantum simulation across 50 independent runs per method, with rigorous statistical validation including paired t-tests, Wilcoxon signed-rank tests, bootstrap 95% confidence intervals, and formal effect size estimation. Results are reported with full timing decomposition separating quantum circuit execution (T 1 ), classical optimiser time (T 2 ), and infrastructure overhead (T 3 ). The central finding is that the Adaptive Hybrid Quantum-Classical model with a Hardware-Efficient Ansatz (Hybrid QC-HEA) achieves a mean 4DVAR cost of 2.10 on L63 and 21.0 on L96 representing only 11.7% and 14.8% above the Classical 4DVAR baseline respectively—differences that are not statistically significant at p < 0.05. Crucially, Hybrid QC-HEA outperforms all three deep learning baselines by substantial margins on L96, achieving 5.5x lower cost than DA-LSTM, 5.2x lower than LSTM, and 8.3x lower than Neural ODE. The Hybrid QC-HEA also exhibits the tightest cost distribution across 50 runs on L96, demonstrating superior operational reliability compared to all competing methods. Conversely, all-quantum VQE-based methods with no refinement by classical methods scale to cost 32 and 75x more than classical on L96, and thus gradient-free quantum optimisation without the classical BFGS refinement step is ultimately impractical to high-precision data assimilation and the classical BFGS refinement step is in any case a fundamental element of the architecture. Computational scaling analysis reveals that Classical 4DVAR wall-clock time grows 126-fold from L63 to L96, consistent with theoretical predictions of exponentially increasing complexity in chaotic optimisation landscapes, while the hybrid framework maintains near-classical accuracy at both scales. These results constitute an empirical proof-of-concept for hybrid quantum-classical data assimilation on realistic atmospheric models, establishing a reproducible benchmarking framework for future investigation on near-term quantum processors based NISQ devices.
Numerical Weather Prediction (NWP) refers to the use of mathematical models to simulate the atmosphere's behavior and predict weather conditions. These models are based on the fundamental laws of physics and dynamics, integrated using initial atmospheric observations. Pioneers like Lewis Fry Richardson and Edward Lorenz laid the foundation of modern weather prediction. Parametrization involves replacing complex or unresolved physical processes (e.g., cloud formation, turbulence) with simplified models. It enhances computational efficiency and model realism. Quantum computing leverages quantum bits (qubits), which exist in superpositions and exhibit entanglement. Quantum gates manipulate qubits, and circuits' process quantum information. Quantum computing offers a way to solve high-dimensional, nonlinear systems more efficiently, crucial for parametrization in weather models. In this paper we discuss the quantum computing, though nascent, shows strong potential in enhancing the accuracy and efficiency of weather forecasting through refined parametrization.
We propose a novel hybrid quantum-classical framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) and Quantum-enhanced Markov Chain Monte Carlo (QMCMC) with variational particle filters to tackle the computational challenges in Four-Dimensional Variational Data Assimilation (4DVAR). 4DVAR, widely used in numerical weather prediction, suffers from inefficiencies in high-dimensional, non-linear systems. Our approach, the Quantum Variational Particle Filter (QVPF), uses QAOA to optimize particle proposals and QMCMC to efficiently compute particle weights and resample, accelerating convergence while reducing the computational load. The QVPF framework addresses the curse of dimensionality by minimizing the number of particles required for accurate state estimation, thus improving efficiency in systems with complex dynamics. The hybrid model offers enhanced accuracy by integrating quantum algorithms into the variational particle filter, making it particularly suited for applications in climate modeling, space weather prediction, and defense. The potential for achieving unprecedented resolution in predictive models could transform sectors that rely on high-resolution forecasting. We present the mathematical foundations of the approach, along with discussions on algorithmic implementation and hardware requirements. Early results suggest that this hybrid framework could significantly improve data assimilation, with future implementations on near-term quantum devices offering a practical pathway for scaling up. This work demonstrates how quantum computing can address the growing need for more accurate and computationally feasible methods in large-scale data assimilation.
To date, conventional computers have never been able to efficiently handle certain tasks, where the number of computation steps is likely to blow up as the problem size increases. As an emerging technology and new computing paradigm, quantum computing has a great potential to tackle those hard tasks efficiently. Among all the existing quantum computation models, quantum annealing has drawn significant attention in recent years due to the realization of the commercialized quantum annealer, sparking research interests in developing applications to solve problems that are intractable for classical computers.However, designing and implementing algorithms that manage to harness the enormous computation power from quantum annealer remains a challenging task. Generally, it requires mapping of the given optimization problem into quadratic unconstrained binary optimization(QUBO) problem and embedding the subsequent QUBO onto the physical architecture of quantum annealer. Additionally, practical quantum annealers are susceptible to errors leading to low probability of the correct solution.In this study, we focus on solving Boolean satisfiability (SAT) problem using quantum annealer while addressing practical limitations. We have proposed a mapping technique that maps SAT problem to QUBO, and we have further devised a tool flow that embeds the QUBO onto the architecture of a quantum annealing device. Additionally, We have optimized the proposed embedding flow to reduce run-time in addition to shortening the qubit chain length, leading to robust quantum annealing. To further improve the reliability of quantum annealing, we have also developed a post processing embedding technique that enlarges the energy gap between ground state and the first excited state. To demonstrate the effectiveness of proposed methods, we have conducted experiments on real quantum annealing devices manufactured by D-Wave Systems, showing compelling result of using quantum annealer to solve SAT problem.
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.
Modern businesses are facing more and more challenges in terms of Big Data warehousing and real-time data analytics due to the sheer volume of growing data. Traditional optimization techniques are increasingly ineffective when working with high-dimensional datasets, thus creating delays in resource allocation and query processing. Since there is a growing demand for faster solutions for data analytics, it is necessary to find new methods for solving optimization issues. In this respect, new emerging quantum-inspired computing techniques allow solving complex optimization problems by employing the principles of quantum mechanics—superposition and probability exploration. To enhance the performance of systems used for predictive analytics and data warehousing, a quantum-inspired optimization framework is proposed. This approach involves incorporating quantum-inspired techniques such as simulations of quantum annealing processes into frameworks used for distributed processing, thus resulting in the improvement of the areas of data indexing, query execution paths and load balancing of computers. The data processing machines are improved due to the advancements in feature selection and attainment of results in a faster way. Evaluation of the method on the big datasets showed that the query performance, and the accuracy of prediction is higher than that demonstrated by conventional techniques, and the architecture is efficient and can be scaled for processing the workloads for real-time analytics.