quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computationalfluiddynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive ...
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quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computationalfluiddynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "IterativeQLS"that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than 0.2%, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.
In this paper we present a scalable algorithm for fault-tolerant quantum computers for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities, where the obje...
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In this paper we present a scalable algorithm for fault-tolerant quantum computers for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities, where the object walls are aligned with the Cartesian grid, the relative difference of velocities in each dimension is bounded by 1 and the total simulated time is dependent on the discrete velocities chosen. We provide detailed descriptions and complexity analyses of all steps of our quantum transport method (QTM) and present numerical results for 2D flows generated in Qiskit as a proof of concept. Our QTM is based on a novel streaming approach which leads to a reduction in the amount of CNOT gates required in comparison to state-of-the-art quantum streaming methods. As a second highlight of this paper we present a novel object encoding method, that reduces the complexity of the amount of CNOT gates required to encode walls, which now becomes independent of the size of the wall. Finally we present a novel quantum encoding of the particles' discrete velocities that enables a linear speed-up in the costs of reflecting the velocity of a particle, which now becomes independent of the amount of velocities encoded. Our main contribution consists of a detailed description of a fail-safe implementation of a quantum algorithm for the reflection step of the transport equation that can be readily implemented on a physical quantum computer. This fail-safe implementation allows for a variety of initial conditions and particle velocities and leads to physically correct particle flow behavior around the walls, edges and corners of obstacles. Combining these results we present a novel and fail-safe quantum algorithm for the transport equation that can be used for a multitude of flow configurations and leads to physically correct behavior. ( ) We finally show that our approach only requires O ������������������2 ������+ ������������������������ ������2CNOT gates, which is ������ max
The paper presents physical principles, basic concepts, analytical methods and the applications of quantumfluid mechanics for the examination of the behaviors of atoms, molecules and quantum systems, with an emphasis...
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The paper presents physical principles, basic concepts, analytical methods and the applications of quantumfluid mechanics for the examination of the behaviors of atoms, molecules and quantum systems, with an emphasis focused on complementing the ontological interpretation of quantum mechanics. quantumfluids, which consist of the probability fluids, obey the laws of conservation derived from the theoretical framework of quantum mechanics but described by alternative mathematical representation. The fluid descriptions of selected quantum systems, quantum slabs, wires and quantum dots, particle emitter, and hydrogen atom are compared with the descriptions of wave formalism of Schrodinger to elucidate non-linear quantum physical phenomena, which have not been treated by the quantum mechanics. Basic fluid dynamic behaviors of various configurations at non-steady state are examined and the dispersion relations at different degrees of quantum effects studied. quantum modal balance theory is developed for the examination of a hydrogen atom. The Coulomb potential is found to be balanced with the parts of the dilatation energy and the kinetic energy of diffusion of probability fluid. The origin of the quantized energy is also identified as the fraction of the kinetic energy of radial diffusion of the fluid. The potential applications of quantumfluiddynamics and quantum computational fluid dynamics to the nanoscience and technology are discussed.
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