This is a thesis in theoretical physics about analog quantum simulations, digital quantum simulations (quantum computing), and quantum state preparation using different quantum platforms (neutral atoms, trapped ions, and superconducting circuits). We live in a quantum era with such a wide variety of platforms available, however performing experiments on existing quantum devices remains challenging due to limitations in control, scale, and connectivity. Therefore, innovative strategies must be developed to achieve quantum advantage using current quantum technology. We are primarily interested in applications to high-energy physics, as quantum computing provides a natural framework for simulating the real-time evolution of gauge theories. While the field of quantum simulations and quantum computing is still in its infancy and may be far from uncovering relevant insights about the Standard Model in regimes inaccessible to analytical methods, classical simulations, or direct experiments, interesting discoveries are emerging. Significant developments include the observation of quantum many-body scar states and the reformulation of quantum field theories as quantum link models. 

Most part of the thesis is dedicated to the quantum simulations of lattice gauge theories, which we explore under different lenses. First, we propose a scheme to effectively generate three body interactions in trapped-ion platforms which consists of a generalization of the Mølmer-Sørensen scheme for three spins. In this project, we envision the quantum simulation of the spin 1/2 quantum link model description of the massless Schwinger model, which features a three-body interaction. Such interaction requires at least 12 two-qubit gates to be performed, which in principle accumulates more errors than a single three-qubit gate. This is what makes analog quantum simulations so powerful: We can tailor the platform to generate interactions of a specific target model, potentially reducing quantum errors. 

Next, assuming the existence of a perfect three-body gate, we study quantum many-body scar states in the Schwinger model. We use a mapping from the spin 1/2 Schwinger quantum link model to the PXP model to identify the relevant physical configurations. Then, we compare the evolution of thermal and non-thermal states under sequential Trotterized quantum circuits to their evolution under randomized quantum circuits. Our results indicate that the non-thermal sector of the Hilbert space, which includes the quantum many-body scars, are more sensitive to randomization. 

Then, on a more realistic note, we use real quantum devices from IBMQ to perform digital quantum simulations of the Schwinger model. These quantum computers are based on superconducting circuits, and we currently have access to up to 156-qubits together with a basis of single and two-qubit gates. The devices impose strong limitations on connectivity and depth of the quantum circuits, hence we propose using gauge invariance, in the form of the Gauss' law, for quantum error detection.

In the last part of this thesis, we shift focus to study an interesting many-body behavior that emerges from the presence of a static gauge field. Specifically, we propose a protocol for the quasi-adiabatic preparation of the 1/2-Laughlin state, a fractional quantum Hall state, using rotating ultracold atoms to create artificial gauge fields. From the condensate phase to the Laughlin state there are three points of closed gaps, and we make trap largely anisotropic to cross these regions without losing fidelity. We improved the preparation times by a factor of ten compared to previous studies.

Tuesday May 27, 10:00 h. ICFO Auditorium

Thesis Directors: Prof. Dr. Maciej Lewenstein and Dr. Tobias Daniel Grass.