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To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Developing quantum algorithms to simulate fluid dynamics has become an active area of research, as accelerating fluid simulations could have significant impact in both industry and fundamental science. While many approaches have been…
Quantum algorithms for classical physics problems expose new patterns of quantum information flow as compared to the many-body Schr\"{o}dinger equation. As a result, besides their potential practical applications, they also offer a valuable…
As the scope of Computational Fluid Dynamics (CFD) grows to encompass ever larger problem scales, so does the interest in whether quantum computing can provide an advantage. In recent years, Quantum Lattice Gas Automata (QLGA) and Quantum…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
QubitSolve is working on a quantum solution for computational fluid dynamics (CFD). We have created a variational quantum CFD (VQCFD) algorithm and a 2D Software Prototype based on it. By testing the Software Prototype on a quantum…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
Digital quantum computers promise exponential speedups in performing quantum time-evolution, providing an opportunity to simulate quantum dynamics of complex systems in physics and chemistry. However, the task of extracting desired quantum…
A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. For the fluid flow equations the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for…
For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…
This paper presents the first application of quantum generative models to learned latent space representations of computational fluid dynamics (CFD) data. While recent work has explored quantum models for learning statistical properties of…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…