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Quantum computing has the potential to solve many computational problems exponentially faster than classical computers. The high shares of renewables and the wide deployment of converter-interfaced resources require new tools that shall…
Developing a systematic view of where quantum computers will outperform classical ones is important for researchers, policy makers and business leaders. But developing such a view is challenging because quantum advantage analyses depend not…
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
Vortex interactions are commonly observed in atmospheric turbulence, plasma dynamics, and collective behaviors in biological systems. However, accurately simulating these complex interactions is highly challenging due to the need to capture…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
While quantum computers promise to solve some scientifically and commercially valuable problems thought intractable for classical machines, delivering on this promise will require a large-scale quantum machine. Understanding the impact of…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer…
Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…
We discuss the Carleman approach to the quantum simulation of classical fluids, as applied to i) Lattice Boltzmann (CLB), ii) Navier-Stokes (CNS) and iii) Grad (CG) formulations of fluid dynamics. CLB shows excellent convergence properties,…
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…
Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…