Sparse Configuration Interaction for the Electronic Schrödinger Equation Revisited: Complete Basis Set Limit Complexity and Quantum-Encoding Impact
For researchers in quantum chemistry and quantum computing, the paper provides theoretical insights that could improve numerical solvers and reduce qubit requirements, though it is largely theoretical and incremental.
The paper revisits regularity results for eigenfunctions of the electronic Schrödinger equation, showing that the curse of dimensionality in convergence to the complete basis set limit can be mitigated, with the main convergence rate term independent of electron number. This suggests potential benefits for classical solvers and quantum-computing approaches via new qubit-efficient encodings.
In this article we revisit regularity results for eigenfunctions in the discrete spectrum of the electronic Schrödinger 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 Schrödinger equation and also for quantum-computing approaches through new qubit-efficient wavefunction encodings.