Title: Robust control of quantum networks down to fundamental limitations

Speaker: Edmond A. Jonckheere

Abstract: Quantum control has the ambition to get down to accuracies never contemplated before. So far emphasis has been put on physical limitations, e.g., Planck length in quantum optical control, but only very recently has it been realized that the spectacular achievements of the universal science of control brings, on the flipside, its own limitations. Our query is whether quantum physics offers loopholes to defeat the fundamental limitations imposed by classical physics (or classical geometry?) in such systems as feedback amplifiers as articulated by Bode, Horowitz, and many followers. As theoretical prototypical platform, we will consider spintronic networks with the objective of “routing” excitation-encoded information for an initial to a terminal spin. Following classical lines, the closed-loop fidelity error will be quantified by a “sensitivity function” that does not architecturally match the one of Bode upon which the fundamental limitations rest. It will be shown that a major classical-quantum discrepancy stems from the presence of the global phase factor in the quantum sensitivity function, which needs to be reinterpreted in the context of projective geometry. Removal of the global phase factor will allow us to examine the quantum-classical discrepancies—with early evidence of the possibility to have minimum fidelity error coexisting with minimum sensitivity of fidelity error, contrary to classical expectations. A data base of results was developed where fidelity and sensitivity of fidelity were shown to be concordant using nonparametric rank ordering tests. Finally, it will be shown that classicality, that is, discordance between fidelity and sensitivity of fidelity, reappears under decoherence.

(This is joint work with S. Schirmer (Swansea Univ., UK), F. Langbein (Cardiff Univ., UK), and C. Weidner (Aarhus University, Denmark), partially supported by NSF IRES 1829078.)