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Item type:Publication, Access status: with files , Quantum-inspired tensor-network fractional-step method for incompressible flow in curvilinear coordinates(Elsevier, 2026-04-22); ; ; ; We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.Publicationtype: Journal Article48 12 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Toward variational quantum algorithms for generalized linear and nonlinear transport phenomena(American Institute of Aeronautics and Astronautics (AIAA), 2026-02); ; ; This article proposes a variational quantum algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers’ equations in combination with different engineering boundary conditions. Topics covered include the encoding of band matrices, as in the consideration of nonconstant material properties and upwind-biased first- and higher-order approximations, widely used in engineering computational fluid dynamics, by the use of a mask function. Verification examples demonstrate high predictive agreement with classical methods. Furthermore, the scalability analysis shows a polylog scaling of the number of quantum gates with the number of qubits. Remaining challenges refer to the implicit construction of upwind schemes and the identification of an appropriate parameterization strategy of the quantum ansatz.Publicationtype: Journal Article67 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Boundary treatment for variational quantum simulations of partial differential equations on quantum computers(Elsevier, 2025); ; ; ; The paper presents a variational quantum algorithm to solve initial–boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum framework that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with a modular control-to-state operator (ansatz). The objective function and its derivatives required by the optimizer can efficiently be evaluated on a quantum computer by measuring an ancilla qubit, while the optimization procedure employs classical hardware. The focal aspect of the study is the treatment of boundary conditions, which is tailored to the properties of the quantum hardware using a correction technique. For this purpose, the boundary conditions and the discretized terms of the partial differential equation are decomposed into a sequence of unitary operations and subsequently compiled into quantum gates. The accuracy and gate complexity of the approach are assessed for second-order partial differential equations by classically emulating the quantum hardware. The examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results of this flexible approach display a robust behavior and a strong predictive accuracy in combination with a remarkable polylog complexity scaling in the number of qubits of the involved quantum circuits. Remaining challenges refer to adaptive ansatz strategies that speed up the optimization procedure.Publicationtype: Journal Article46 56 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Variational quantum algorithms for computational fluid dynamics(American Institute of Aeronautics and Astronautics (AIAA), 2023-03-09); ; ; Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required hardware but also in identifying the most promising application areas and developing the corresponding quantum algorithms. The availability of intermediate-scale noisy quantum computers is now propelling the developments of novel algorithms, with applications across a variety of domains, including in aeroscience. Variational quantum algorithms are particularly promising because they are comparatively noise tolerant and aim to achieve a quantum advantage with only a few hundred qubits. Furthermore, they are applicable to a wide range of optimization problems arising throughout the natural sciences and industry. To demonstrate the possibilities for the aeroscience community, we give a perspective on how variational quantum algorithms can be used in computational fluid dynamics. We discuss how classical problems are translated into quantum algorithms and their logarithmic scaling with problem size. For an explicit example, we apply this method to Burgers’s equation in one spatial dimension. We argue that a quantum advantage over classical computing methods could be achieved by the end of this decade if quantum hardware progresses as currently envisaged and emphasize the importance of joining up development of quantum algorithms with application-specific expertise to achieve a real-world impact.Publicationtype: Journal Article70