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Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical…
In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, non-interacting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we…
Accurate simulation to dynamics of axial piston pump (APP) is essential for its design, manufacture and maintenance. However, limited by computation capacity of CPU device and traditional solvers, conventional iteration methods are…
We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…
Computational physics is an important tool for analysing, verifying, and -- at times -- replacing physical experiments. Nevertheless, simulating quantum systems and analysing quantum data has so far resisted an efficient classical treatment…
We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the…
Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
Particle accelerators are invaluable tools for research in the basic and applied sciences, in fields such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid…
We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the…
Transient stability simulation of a large-scale and interconnected electric power system involves solving a large set of differential algebraic equations (DAEs) at every simulation time-step. With the ever-growing size and complexity of…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…