Quantum State Generation in Mesoscopic Systems of Photons and Atoms

Abstract

Besides the genuine interest in investigation of natural phenomena, the possibility of exploiting properties of quantum theory for technical improvements, by achieving a more efficient manipulation, readout and transmission of the information, resulted one of the main drivers that attracted the interest of public opinion and led to incessant research in this field both from public and private organizations. In principle, quantum superposition and entanglement, once handled the intrinsic limits of quantum theory, such as no-cloning theorem and uncertainty principle, would guarantee a scaling advantage of quantum computation over its classical counterpart. While the quantum advantage becomes more important with the dimensionality of the algorithm that is used, the computation itself becomes proportionally more sensitive to the undesired interactions with the environment and thus prone to errors. The research conducted to prove the working principles of quantum schemes, being sources, algorithm or measurements is thus conveniently realized on mesoscopic scale system where the dimension cardinality of the setup is big enough to show a significative advantage over classical schemes but constrained as well to be described either analytically or through numerical simulations, or experimentally realized in a research laboratory. Specific criteria for efficient quantum computation have been introduced in 1996 by David DiVincenzo, they include conditions on the physical system to encode the information, the ability to prepare the system in a given quantum states, long coherence times, a universal set of quantum gates, and the ability of measuring the qubits the state preparation. This thesis deals with the second of the DiVincenzo’s criteria, by investigating the state preparation of quantum states using linear optics and Rydberg atoms. Disposing of universal and efficient sources of quantum states is indeed crucial to perform versatile fault tolerant quantum computation. In fact, producing quantum states with high fidelity allows to perform more accurate computation. Similarly, the source must be reliable to guarantee that the least amount of decoherence, occurs while waiting for the next quantum state. Universal quantum computation in photonic implementation can be realized only with non-gaussian resources. In this thesis, we propose to alternative schemes to produce non-Gaussian quantum states to produce any general non-Gaussian quantum state with higher levels of fidelity and success probability compared to those achievable by the current conditional sources. It is given also an exact description of the Gottesman-Kitaev-Preskill states produced by the breeding protocol, comparing the results with numerical simulations and the Gaussian Random Noise description that is used to parametrize the non-ideal GKP states produced by this protocol. Finally, a universal protocol to prepare a quantum states or circuit with arbitrary fidelity using Rydberg atoms is introduced.