Related papers: Special Functions and HHL Quantum Algorithm for So…
We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with…
We consider a class of bulk-surface coupled Cahn-Hilliard systems in a smooth, bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, where the trace value of the bulk phase variable is connected to the surface phase variable via a…
We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…
The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include…
We investigate the quantum equation of motion (qEOM), a hybrid quantum-classical algorithm for computing excitation properties of a fermionic many-body system, with a particular emphasis on the strong-coupling regime. The method is designed…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the…
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} ,…
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…
We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms.…
Eshelby's inclusion problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically…
The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and…
A numerical algorithm to calculate exact finite-temperature spectra of many-body lattice Hamiltonians is formulated by combining the typicality approach and the shifted Krylov subspace method. The combined algorithm, which we name…
Here the ionization and high harmonic generation in Hydrogen and Helium by using quantum (hydrodynamic) trajectories is analyzed theoretically. The quantum trajectories allow a self-contained treatment of the electron exchange and…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
It is shown that the atom-molecule collision problem in the presence of an external electric field can be solved using the total angular momentum representation in the body-fixed coordinated frame, leading to a computationally efficient…
Recent experiments at the nanoscales confirm that thermal rectifiers, the thermal equivalent of electrical diodes, can operate in the quantum regime. We present a thorough investigation of the effect of different particle exchange…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
Thermodynamic trade-off relations dictate fundamental limits on the performance of thermodynamic tasks through costs such as heat dissipation. Here, we propose a framework called thermodynamic recycling to circumvent these limits in quantum…
Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared…