Validation of the five-electron pO qubit in Si using full configuration interaction

Abstract

The $pO$ qubit is a recently proposed charge qubit consisting of five electrons confined in a gate-defined Si quantum dot. Because its two qubit states have no dipole moment, it couples to electric fields only through the quadrupole moment, suppressing the dominant decoherence channel of conventional charge qubits while retaining all-electrical control. The original proposal was formulated in a shell-filling picture without Coulomb interactions. In this work we perform full configuration interaction (FCI) calculations to assess the impact of the Coulomb interaction on the viability of the $pO$ qubit. We find that the interacting eigenstates occupy orbital shells beyond the shell-filling picture, with the degree of excitation governed by the competition between valley splitting, orbital energy, and Coulomb energy scales. Additionally, we find that the ground states form degenerate doublets, but of two distinct kinds. Above a crossover near a valley splitting of $E_{\rm{VS}}\approx50~μ$eV the doublet is a pair of orbital angular momentum excitations with $|\langle L_z\rangle|=1$ in the lower valley, while below the crossover the doublet is a pair of single valley excitations with $\langle L_z\rangle=0$. Despite this substantial departure from the shell-filling picture, for $E_{\rm{VS}} > 50~μ$eV the essential features, vanishing dipole moments and nonzero quadrupole tensor between qubit states are preserved. We show that the vanishing dipole is in fact guaranteed by the symmetry properties of the five-electron Hamiltonian. The same energy scales that govern the orbital occupation also set the quadrupole tensor elements and the first excited state energy gap, both of which are in principle tunable through device engineering.