Dissecting simultaneous exchange from modeled multi-dot multi-electron energy spectra

Deliberate simultaneous activation of exchange between multiple electrons facilitates qubit encodings with enhanced operability and noise resilience. In the proverbial three-electron decoherence-free subspace, it adds continuous steering of the exchange direction to the control of the exchange strength, and suppresses leakage. Clearly, superexchange/mediated exchange tune-ups also rely on it.

Full Configuration Interaction (FCI) methods allow controlled accuracy calculations of multi-dot multi-electron states, with the exchange strength being just one of the gaps in the numerically resolved energy spectrum. But the exchange direction is inscribed in the FCI eigenstates, and is not easily accessible.

We discuss recovering of this information by partitioning the total exchange into its pairwise constituents, in more complicated scenarios with the help of the solution to the specially formulated auxiliary problem. The method is applied to the analysis of exchange in present-day Si/SiGe triangular TQD and SiMOS 2x2 square plaquette devices, as well as the effect of a nearby neutral donor on exchange operations in a dot array.