Séminaire du LPTMS : Nicolò Beato (MPIPKS, Dresden)

Control landscape phase transitions (CLPTs) occur as abrupt changes in the cost function landscape upon varying a control parameter and can be revealed by non-analytic points in statistical order parameters [1]. A prime example are quantum speed limits (QSL) which mark the onset of controllability as the protocol duration is increased.

In this talk, I present results from recent works introducing analytical and numerical methods designed to study CLPTs [2-3]:

(i) Analytical expansions: we lay the foundations of an analytical theory for CLPTs by developing different analytical expansions for the cost function that capture the behavior of CLPTs with controlled precision;

(ii) Stability analysis: we show that CLPTs can be associated with different types of instabilities of the optimal protocol; this allows us to explicitly relate CLPTs to critical structural rearrangements in the extrema of the control landscape

(iii) Universality of QSL transition: utilizing path integral methods from statistical field theory, we trace back the critical scaling of the order parameter at the QSL to the properties of the set of optimal protocols

(iv) Topological CLPTs: we introduce a numerical sampling algorithm designed to explore the set of optimal protocols via homotopic stochastic update rule; this verifies our analytical predictions and reveals the existence of a new class of CLPTs, of topological nature, associated with sharp experimental signatures.

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[1] Phys. Rev. Lett. 122, 020601
[2] arXiv:2408.11110
[3] arXiv:2411.08736