Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers

The data refers to a variational quantum algorithm experiments solving initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware 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 examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results are complemented by classical finite difference results, which have been taken for comparison in the underlying document (arXiv.2402.18619).