Sparse Configuration Interaction for the Electronic Schr\"odinger Equation Revisited: Complete Basis Set Limit Complexity and Quantum-Encoding Impact

In this article we revisit regularity results for eigenfunctions in the discrete spectrum of the electronic Schr\"odinger equation and study their consequences for approximation complexity. In particular, for the convergence to the complete basis set limit, it can be shown that the curse of dimensionality in the leading algebraic exponent can be mitigated. That is, for general sparse grid constructions, the main term of the convergence rate with respect to the number of degrees of freedom is independent of the number of electrons. These insights indicate potential benefits for classical numerical solvers of the electronic Schr\"odinger equation and also for quantum-computing approaches through new qubit-efficient wavefunction encodings.