Showing papers by "Stéphane Guérin published in 2022"

Optimal robust stimulated Raman exact passage by inverse optimization

Abstract: We apply the inverse geometric optimization technique to generate an optimal and robust stimulated Raman exact passage (STIREP) considering the loss of the upper state as a characterization parameter. Control fields temporal shapes that are optimal with respect to pulse area, energy, and duration, are found to form a simple sequence with a combination of intuitively (near the beginning and the end) and counter-intuitively ordered pulse pairs. The resulting dynamics produces a loss which is about a third of that of the non-robust optimal STIREP. Alternative optimal solutions featuring lower losses, larger pulse areas, and fully counter-intuitive pulse sequences are derived.

Optimal quantum control robust against pulse inhomogeneities: Analytic solutions

Abstract: We study optimal quantum control robust against pulse inhomogeneities for various partial population transfers and single-qubit gates by inverse optimization. We show that the pulse is constant for time or energy minimization and we provide the analytic form of the detuning as Jacobi elliptic cosines. The performance of composite pulse techniques, which we optimize for the case of complete population transfer, is compared to this optimal bound.

Robust quantum control by smooth quasi-square pulses

Abstract: Robust time-optimal control is known to feature constant (square) pulses. We analyze fast adiabatic dynamics that preserve robustness by using alternative smooth quasi-square pulses, typically represented by hyper-Gaussian pulses. We consider here the two protocols, robust inverse optimization and time-contracted adiabatic passage, allowing the design of the same pulse shape in both cases. The dynamics and their performance are compared. The superiority of the former protocol is shown.

Space-time propagation of photon pulses in dielectric media, illustrations with beam splitters

Abstract: Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic configurations can be constructed by linear combinations. In this presentation we discuss a formulation constructed in the general formalism of bosonic Fock space, in which the quantum excitation can be constructed directly on localized pulses of arbitrary shape. Although the two formulations are essentially equivalent, the direct formulation in terms of pulses has some conceptual and practical advantages, which we illustrate with some examples. The first one is the passage of a single photon pulse through a beam splitter. The analysis of this formulation in terms of pulses in Fock space shows that there is no need to introduce ‘vacuum fluctuations entering through the unused port’, as is often done in the literature. Another example is the Hong–Ou–Mandel effect. It is described as a time dependent process in the Schrödinger representation in Fock space. The analysis shows explicitly how the two essential ingredients of the Hong–Ou–Mandel effect are the same shape of the pulses and the bosonic nature of photons. This formulation shows that all the phenomena involving linear quantum optical devices can be described and calculated on the basis of the time dependent solution of the corresponding classical Maxwell’s equations for pulses, from which the quantum dynamics in Fock space can be immediately constructed.

Robust digital optimal control on IBM quantum computers

Abstract: The ability of pulse-shaping devices to generate accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose and demonstrate a systematic procedure to design robust digital control processes adapted to such experimental constraints. We show to what extent this digital pulse can be obtained from its continuous-time counterpart. A remarkable efficiency can be achieved even for a limited number of pulse parameters. We exper-imentally implement the protocols on IBM’s quantum computers for a single qubit, obtaining an optimal robust transfer in a time T = 382 ns.

Characterization of a Driven Two-Level Quantum System by Supervised Learning

Abstract: We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.