Quantum computing may help reduce computational costs of simulating large and nonlinear systems, but research into the use of quantum computers in atmospheric and oceanic sciences is still at an early stage. This study explores the use of quantum computing for calculating the collision-coalescence process that dominates the size growth of liquid particles in cloud microphysics. Inspired by the quantum algorithms developed in the field of financial engineering, we propose a new algorithm based on a master equation that describes the time evolution of the droplet mass distribution. Our algorithm uses the quantum amplitudes to encode the probability distribution of droplet mass and calculates the expected number of droplets via the quantum amplitude estimation. The key contribution is an encoding strategy that maps the multivariate collision-coalescence problem onto a quantum computation by recording only the transition history rather than the full mass distributions at every time step. This approach reduces the per-step qubit cost from $O(\sqrt{N})$ to $O(\log N)$ , where $N$ is the number of mass bins. Our resource analysis shows that the number of T gates (T-count) scales as $\widetilde{O}(N^2)$ per mass bin in $N$ , for a fixed number of time steps and a given target accuracy, where the $\widetilde{O}$ notation suppresses polylogarithmic factors in $N$ . This is a substantial improvement over classical master-equation methods, whose cost grows super-polynomially with $N$ as the number of possible states increases. Our results suggest that the collision-coalescence process is one of the promising targets of quantum computing in the field of atmospheric science.Quantum computing may help reduce computational costs of simulating large and nonlinear systems, but research into the use of quantum computers in atmospheric and oceanic sciences is still at an early stage. This study explores the use of quantum computing for calculating the collision-coalescence process that dominates the size growth of liquid particles in cloud microphysics. Inspired by the quantum algorithms developed in the field of financial engineering, we propose a new algorithm based on a master equation that describes the time evolution of the droplet mass distribution. Our algorithm uses the quantum amplitudes to encode the probability distribution of droplet mass and calculates the expected number of droplets via the quantum amplitude estimation. The key contribution is an encoding strategy that maps the multivariate collision-coalescence problem onto a quantum computation by recording only the transition history rather than the full mass distributions at every time step. This approach reduces the per-step qubit cost from $O(\sqrt{N})$ to $O(\log N)$, where $N$ is the number of mass bins. Our resource analysis shows that the number of T gates (T-count) scales as $\widetilde{O}(N^2)$ per mass bin in $N$, for a fixed number of time steps and a given target accuracy, where the $\widetilde{O}$ notation suppresses polylogarithmic factors in $N$. This is a substantial improvement over classical master-equation methods, whose cost grows super-polynomially with $N$ as the number of possible states increases. Our results suggest that the collision-coalescence process is one of the promising targets of quantum computing in the field of atmospheric science.

quant-pharXiv:2603.06353Mar 9, 20260 citations

QUANTUM COMPUTING: THE COMPUTING TECHNOLOGY OF TOMORROW

Ms. Gaganpreet Kaur Dr. Mohammed Bakhtawar Ahmed

Redshine ArchiveJul 7, 20240 citations

ADVANCING COMPUTATIONAL MATHEMATICAL MODELING: INTEGRATING QUANTUM COMPUTING AND AI-DRIVEN OPTIMIZATION FOR COMPLEX SYSTEM SIMULATIONS

Asia Ameen, Mujahid Iqbal, Shahzeb Mehmood +3 more

Over the years, computational mathematical modeling has become an important tool in many fields of science, making use of contemporary numerical methods,AI and optimization techniques. This research investigates the underlying computational methodologies in practical mathematical modeling, spanning finite element techniques, differential equation solvers, as well as machine learning-based prediction models. Theoretical content covered includes probability theory, statistical modeling and differential equations, all used to represent complex real-world systems. The Diedrichs study exposes the use of computational models in various disciplines such as physics, engineering, biology, medicine,finance, and environmental science used for structural analysis, disease modeling, risk assessment, and climate simulation. Despite tremendous progress, challenges such as computational inefficiency, model accuracy bounds, and scalability persist. AI, quantum computing, and hybrid models are new technologies that can be potential responses to these limitations, providing opportunities for computational efficiency and predictive accuracy improvements. Future studies should be directed towards improving computation algorithms through adaptive algorithms, combining multiple disciplines (i.e., biology, engineering) to address complex problems, and employing high-performance computing techniques. Adaptive technology's mathematical modeling is also going to evolve, thus, adding to the jumps in scientific progress (more realistic simulation or data-based decision on complex systems). With these ideas and the novel computational paradigms that they may enable, this will guarantee the continued evolution of this field, which holds the keys to unleashing an innovation engine for science, engineering, and applied mathematics.Over the years, computational mathematical modeling has become an important tool in many fields of science, making use of contemporary numerical methods,AI and optimization techniques. This research investigates the underlying computational methodologies in practical mathematical modeling, spanning finite element techniques, differential equation solvers, as well as machine learning-based prediction models. Theoretical content covered includes probability theory, statistical modeling and differential equations, all used to represent complex real-world systems. The Diedrichs study exposes the use of computational models in various disciplines such as physics, engineering, biology, medicine,finance, and environmental science used for structural analysis, disease modeling, risk assessment, and climate simulation. Despite tremendous progress, challenges such as computational inefficiency, model accuracy bounds, and scalability persist. AI, quantum computing, and hybrid models are new technologies that can be potential responses to these limitations, providing opportunities for computational efficiency and predictive accuracy improvements. Future studies should be directed towards improving computation algorithms through adaptive algorithms, combining multiple disciplines (i.e., biology, engineering) to address complex problems, and employing high-performance computing techniques. Adaptive technology's mathematical modeling is also going to evolve, thus, adding to the jumps in scientific progress (more realistic simulation or data-based decision on complex systems). With these ideas and the novel computational paradigms that they may enable, this will guarantee the continued evolution of this field, which holds the keys to unleashing an innovation engine for science, engineering, and applied mathematics.

Policy Research JournalMay 15, 20250 citations

What is Quantum Computing

Kevin A. Yuh

Jan 1, 20125 citations

O(\sqrt{N})

O(\log N)

, where

N

is the number of mass bins. Our resource analysis shows that the number of T gates (T-count) scales as

\widetilde{O}(N^2)

per mass bin in

N

, for a fixed number of time steps and a given target accuracy, where the

\widetilde{O}

notation suppresses polylogarithmic factors in

N

. This is a substantial improvement over classical master-equation methods, whose cost grows super-polynomially with

N

as the number of possible states increases. Our results suggest that the collision-coalescence process is one of the promising targets of quantum computing in the field of atmospheric science.