Controllable Approximations for Spin Qubit Design - Jacob's Ladder of Device Modelling

Some key quantities for spin qubits - tunnel rates, exchange coupling and electronic correlations in general - are hard to describe within the most commonly adopted approximations. Tunnel rates and the exchange coupling are small corrections to the total electronic energy, so that variational methods often fail to predict these quantities. Electronic correlations can be accurately calculated for few electrons through full CI, for example, but are difficult for many electrons. We discuss some of the limitations of these approaches and how to overcome these with state-of-the-art methods that are controllable. We review two methods to improve the accuracy of these quantities: the Path Integral Monte Carlo method for tunnel rates and exchange coupling; and the Density Functional Theory applied to the effective mass Hamiltonian for the many electron problem. Both methods have controllable approximations that may be systematically improved by enhancing the computational effort.