Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical-quantum framework that reformulates a data-assimilation-augmented parameter estimation problem as a combinatorial optimization task. Model dynamics and data assimilation are enforced entirely on the classical side, while the resulting parameter estimation cost functional is discretized and approximated by a quadratic unconstrained binary optimization (QUBO) surrogate. This surrogate is mapped to an Ising Hamiltonian, and quantum optimizers are used to search for low-energy configurations corresponding to candidate parameter estimates. We apply the framework to SIS and SIR epidemic models, the chaotic Lorenz-63 system, and a high-dimensional two-layer Lorenz-96 system. In this setting, the method is used to recover classical system parameters from partial state observations across steady-state, chaotic, and high-dimensional multiscale dynamical systems. Numerical experiments with synthetic data show that the proposed approach accurately recovers parameters while requiring data-assimilation solves only on a prescribed coarse grid. The framework avoids quantum state tomography, illustrating a viable pathway for integrating quantum optimization into data-driven parameter estimation for nonlinear dynamical systems.
Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical-quantum framework that reformulates a data-assimilation-augmented parameter estimation problem as a combinatorial optimization task. Model dynamics and data assimilation are enforced entirely on the classical side, while the resulting parameter estimation cost functional is discretized and approximated by a quadratic unconstrained binary optimization (QUBO) surrogate. This surrogate is mapped to an Ising Hamiltonian, and quantum optimizers are used to search for low-energy configurations corresponding to candidate parameter estimates. We apply the framework to SIS and SIR epidemic models, the chaotic Lorenz-63 system, and a high-dimensional two-layer Lorenz-96 system. In this setting, the method is used to recover classical system parameters from partial state observations across steady-state, chaotic, and high-dimensional multiscale dynamical systems. Numerical experiments with synthetic data show that the proposed approach accurately recovers parameters while requiring data-assimilation solves only on a prescribed coarse grid. The framework avoids quantum state tomography, illustrating a viable pathway for integrating quantum optimization into data-driven parameter estimation for nonlinear dynamical systems.
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.
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.
The rapidly increasing number of heterogeneous data ecosystems, such as structured databases, semi-structured data lakes, real-time streams, distributed knowledge graphs, has further complicated the issue of query planning and optimization in modern information systems extensively. The optimization of queries is essentially an NP-hard combinatorial problem especially when based on multi-join queries, distributed execution plan, dynamic cost model, and uncertainty in the data access patterns. Even decades of concept and engineering advances, classical database optimizers are rapidly becoming unable to offer a globally optimal execution plan when faced with high-dimensional data, high data volatility, with a very tight latency constraint. Good news Recent breakthroughs in quantum computing propose promising computational paradigms that can be used to solve combinatorial optimization problems via quantum parallelism, superposition, and entanglement. Nevertheless, even the near-term quantum hardware is limited in the number of available qubits, noise, and decoherence, making it impractical to achieve fully quantum database systems in any perceived future. This is also the reason why quantum-classical hybrid algorithms are being developed: designed to add quantum optimization subroutines to classical database architectures is guaranteed without breaking their compatibility with existing execution engines. The following paper presents a framework of scalable quantum-classical hybrid computing of complex query planning in heterogeneous data ecosystems. The framework breaks down query optimization into classical and quantum-amenable optimization, which allows NP-hard subproblems, such as join ordering, operator placement, and cost minimization, to be transformed into quantum optimization models such as Quadratic Unconstrained Binary Optimization (QUBO) and Ising Hamiltonians. Classical elements handle query parsing, semantic analysis, constraint verification, and orchestration, whereas quantum processors are called selectively to solve combinatorial decision-making tasks. The suggested architecture will consist of a layered execution, hybrid execution, cost-model encoding approach, and adaptive fallback mechanisms to make them robust to quantum hardware variability. This has been experimentally tested with simulated quantum annealing and variational quantum algorithms that exhibit a quantifiable improvement in the quality and scalability of optimization and heuristics based on entirely classical algorithms, especially in high-dimensional query plans. The findings confirm the practicability of quantum query optimization and put down a feasible route to implement quantum algorithms in the serving machine of the next-generation data management systems.
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.
This paper introduces a novel high-order quantum adaptive algorithm parameter optimization framework. Traditional parameter optimization methods often rely on static adjustments, failing to fully leverage the dynamic behavior of quantum systems. Our framework dynamically adjusts quantum parameters based on real-time quantum computation results, offering a more effective optimization strategy. We propose a method that integrates optimization with quantum system dynamics, allowing for adaptive parameter tuning. This innovation aims to significantly enhance the performance of quantum algorithms by intelligently adjusting quantum parameters during the computation process. The proposed framework demonstrates improved results across a range of benchmark problems, showcasing its potential for advancing quantum computational capabilities.
Quantum computing offers potential advantages for solving partial differential equations (PDEs). However, most existing quantum PDE solvers primarily focus on preparing quantum states for solutions, while the efficient recovery of classical information from these states remains less explored. Motivated by the readout limitation, we propose a quantum-classical hybrid framework for Bayesian PDE inversion problems: The quantum processor evolves the PDE and evaluate the loss function with sampling noises, while the classical computer tunes the hyper-parameters in the Gaussian Process Regression to explore the next trial candidate. To match the quantum solvers for linear and semi-linear autonomous evolution PDEs, we suggest to use a normalized quantum-state loss as the data-misfit function and evaluate the new misfit by combining quantum PDE solvers with the Hadamard test, thereby allowing us to extract useful classical information using only a limited number of quantum state copies without reconstructing the full solution vector. The analysis of error propagation and overall complexity of loss evaluation under a prescribed accuracy shows that the new data-misfit function outperforms the conventional L2-loss under quantum measurements. Quantum circuit simulations of 1D and 2D linear convection diffusion equations under approximate and finite sampling loss evaluations, together with classical numerical experiments on a nonlinear forced viscous Burgers equation, demonstrate the feasibility of the proposed approach for parameter inversion even when the loss evaluations are affected by sampling noise. This framework may provide a viable quantum-assisted scheme for PDE-based inverse problems and elucidate the potential of quantum PDE algorithms in addressing a complete quantum-to-end optimization stack.