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Continuous and Pulsed Quantum Control^{ †}

^{1}

^{2}

^{3}

^{4}

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Strong Continuous Coupling

**Theorem**

**1.**

## 3. Pulsed Decoupling

**Theorem**

**2.**

## 4. Example: Four-Level System

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A pictorial representation of the partitioning of the Hilbert space $\mathcal{H}$ into QZSs ${\mathcal{H}}_{\mu}={P}_{\mu}\mathcal{H}$. If the system is in a given QZS at the initial time ${t}_{0}$, it will evolve coherently in this subspace and will never make a transition to the other QZSs.

**Figure 2.**(

**a**) Alternating free evolutions of duration $t/n$ with instantaneous unitary kicks ${U}_{\mathrm{kick}}$ (

**b**) is equivalent to a sequence of infinitesimal evolutions of duration $t/n$ generated by Hamiltonians ${H}_{\ell}={U}_{\mathrm{kick}}^{\u2020\ell}H{U}_{\mathrm{kick}}^{\ell}$ rotated at each step by the unitary kick.

**Figure 3.**Effect of the strong coupling between states $|3\rangle $ and $|4\rangle $. The other two QZSs have not been highlighted in the figure since they are made of linear combinations of states $|3\rangle $ and $|4\rangle $.

**Figure 4.**Populations ${P}_{k}$ with ${\Omega}_{1}={\Omega}_{2}={\Omega}_{3}\equiv \Omega $ without control potential (

**a**) and with the control potential turned on with $K=100\Omega $ (

**b**).

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**MDPI and ACS Style**

Gramegna, G.; Burgarth, D.; Facchi, P.; Pascazio, S.
Continuous and Pulsed Quantum Control. *Proceedings* **2019**, *12*, 15.
https://doi.org/10.3390/proceedings2019012015

**AMA Style**

Gramegna G, Burgarth D, Facchi P, Pascazio S.
Continuous and Pulsed Quantum Control. *Proceedings*. 2019; 12(1):15.
https://doi.org/10.3390/proceedings2019012015

**Chicago/Turabian Style**

Gramegna, Giovanni, Daniel Burgarth, Paolo Facchi, and Saverio Pascazio.
2019. "Continuous and Pulsed Quantum Control" *Proceedings* 12, no. 1: 15.
https://doi.org/10.3390/proceedings2019012015