Barış Çakmak

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We examine the emergence of dynamical memory effects in quantum processes having indefinite time direction and causal order. In particular, we focus on the class of phase-covariant qubit channels, which encompasses some of the most significant paradigmatic open quantum system models. In order to assess the memory in the time evolution of the system, we utilize the trace distance and the entanglement based measures of non-Markovianity.

We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyze their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to timekeeping errors, and the degradation under environmental noise.