TL;DR
A quantum spectral method for non-periodic boundary value problems with arbitrary Dirichlet boundary conditions is presented, which extends the recently proposed approach by Liu et al. (2024), in which periodic problems are discretised using truncated Fourier series.
Quantum computing offers the potential to solve computational mechanics problems with a more favourable complexity scaling than classically possible. To realise this potential, a quantum-compatible formulation of the finite element method is essential. We present such a formulation for Poisson problems with spatially v...
In this paper, we propose an alternating numerical scheme for constructing quasi-periodic solutions to a class of nonlinear partial differential equations (PDEs) with bounded perturbations, including the one-dimensional nonlinear Schr\"odinger (NLS) equations and nonlinear wave (NLW) equations under periodic and Dirich...
In this work, we develop an accurate numerical homogenization method for computing effective Hamiltonians of quasiperiodic Hamilton--Jacobi equations (QHJEs) with convex Hamiltonians of the form $H(x,p) = |p|^k/{k}-f(x), ~k>1$, where $f$ is quasiperiodic. Computing effective Hamiltonians in the quasiperiodic setting re...
We present a variational quantum linear solver (VQLS) for the Poisson equation built on an exact block encoding of the discrete Laplacian, and demonstrate its performance on physically motivated benchmarks. Unlike LCU-based VQLS where the number of distinct circuits required per cost-function evaluation is $\mathcal{O}...
We present a quantum algorithm for solving partial differential equations through a linear-system formulation, focusing on wave propagation problems described by the discretized Helmholtz equation in frequency domain. Although quantum linear-system solvers offer exponential compression of the system degrees of freedom,...
In previous work, we introduced a semi-analytical method for computing time-domain solutions of linearized Vlasov problems. Rather than representing the plasma response as a sum of residues associated with Landau poles, the method constructs a regularized frequency-domain response spectrum that is subsequently inverted...
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