This seminar will consist of two parts:

- In the first one, I will present three recent proposals on quantum systems where the involvement of a third level in its control protocol has been crucial to open a new avenue for exploitation in computation, sensing or communication.

- In the second part, I will present a method for the analysis and propagation of non-Markovian open quantum systems

For the first part, the proposal concern Andreev Spin Qubits, NV-centers and Trapped Ions.

First, Josephson weak links are known to host Andreev quasiparticles. Their high localization and built-in protection against charge noise makes their spin extremely appealing as registers for quantum information. Nevertheless, their implementation was not possible due to the lack of direct control of the spin state. The final demonstration of such approaches came recently [1] and constitutes ground-breaking progress towards scalable solid-state quantum computers. Thorough analysis of the level structure and the implementation of techniques stemming from quantum optics made it clear that the use of high-lying Andreev modes can be used as intermediaries for the robust coherent control of spin [2]. 

Second, NV-centers in nanodiamonds, which can be used as highly accurate nanoscale sensors, fail to respond to microwave control pulses at low local magnetic fields. With the design of an effective Raman coupling (ERC) [3], it is possible to circumvent this limitation. The ERC can be achieved by adjustment of the microwave frequency to that of the zero-field line and judicious timing of the pulses, such that the full potential of the spin-1 ground state is put to work. The technique has been recently implemented experimentally [4], paving the way for low-field detection of biomolecules.

Finally, trapped ions have long established themselves as accurate and reliable platforms for quantum information processing. Their operation relies on laser cooling preparation steps, which can be substantially improved by the use of electromagnetically-induced transparency [5]. These techniques are flexible and can be designed for complex level structures, as recently shown in quantum-clock experiments [6]. Quantum mass spectrometry experiments will benefit strongly from their implementation [7,8].

For the second part of the talk, I willl present the transfer tensor method for the efficient propagation of non-Markovian open quantum systems

The effect of an environment on an open quantum system is fully described by the memory kernel in the terms presented in the Nakajima-Zwanzig formalism. It contains the key information of its interaction with the environment and, together with the Hamiltonian, it is sufficient to predict the trajectory at later stages. Its computation in realistic settings is nevertheless impractical and it has historically remained a formal result.

We proposed [9] a general approach based on non-Markovian dynamical maps to extract full information from the initial trajectories of a system and compress it into non-Markovian transfer tensors. The non-Markovian transfer tensor method (TTM) is equivalent to solving the Nakajima-Zwanzig equation and, therefore, can be used to reconstruct the dynamical operators (the system Hamiltonian and memory kernel) from quantum trajectories obtained in simulations or experiments and also to accurately and efficiently propagate the state of the system to arbitrarily long time scales.

The concept underlying the approach can be generalized to physical observables such as absorption [10] and emission spectra [11] with the goal of learning and manipulating the trajectories of an open quantum system. From this perspective, it is possible to relate engineered control and steering mechanisms to its corresponding memory kernel so as to determine the architecture of their physical implementations.