Nanotechnology enables the study of various quantum phenomena on real hardware. For instance, semiconducting and superconducting nanostructures can define single-electron transistors, quantum dots, Josephson junctions, and many other examples of quantum devices. It's a wonderful sandbox.
In this thesis, we exploit such a technology to bring the Kitaev chain model to life. The Kitaev Hamiltonian, discussed in the second chapter of this dissertation, describes a chain of N fermionic sites coupled by a standard tunneling and a more exotic superconducting pairing. It is one of the simplest models able to bring the concept of topology into condensed matter physics. Proposed more than twenty years ago, it attracted many experimental groups around the world, due to the promise of realizing a topologically protected qubit. This would be encoded into the Majorana bound states predicted to appear at the ends of the chain. However, such a qubit was never made, due to the difficulty of reproducing the Kitaev model with realistic, hence imperfect, materials.
Here, we demonstrate that engineering Kitaev chains with state-of-the-art materials is possible, by compensating imperfections with fine tuning. As opposed to top-down approaches, this requires building the chain site-by-site and tuning carefully each of them. In this work, each site is represented by a semiconducting quantum dot, while short semiconducting-superconducting hybrids mediate the inter-dot couplings. First, we describe minimal arrays of two quantum dots, show how to control every term of the Kitaev Hamiltonian, and detect the appearance of Majorana bound states. Then, we generalize the tuning procedure to three-site Kitaev chain devices. We also study the additional complications caused by multiple superconductors on the same device.
The main downside of a few-site Kitaev chain is the lack of topological protection. Nevertheless, we demonstrate that its Majorana bound states already exhibit partial protection (against some parameter perturbations), which increases substantially from two- to three-site chains. In the outlook, we propose to generalize the techniques described here to realize a rudimentary Majorana qubit and scale up to even longer Kitaev chains, whose partial protection evolves into topological as N grows.@en

Quantum Batteries (QBs) are quantum-mechanical devices for energy storage, gaining interest due to a potential quantum advantage in power. Recently, the first experimental implementations of QBs were realised. This study characterises the superconducting transmon qubits of Starmon-5 as QBs using the Quantum Inspire platform. In addition to direct charging of a QB, our focus is on charger-mediated energy transfer and parallel charging of an array of transmon qubits. The figures of merit include the average stored energy, the charging time and the charging power.

The results from direct charging of the qubits align with existing literature. Charger-mediated energy transfer is demonstrated through the characterisation of the CNOT gate as an interaction gate, gaining the same amount of stored energy, but with a significant increase in the charging time, resulting in a lower charging power. Furthermore, our findings demonstrate that parallel charging of an array of qubits preserves the quality of direct charging of the individual qubits.

To our knowledge, this work presents the first results of charger-mediated energy transfer in real quantum devices. Charger-mediated energy transfer can be interesting for specific applications such as quantum metrology, where preserving the quantum state is critical. Additionally, this is the first demonstration of parallel charging of superconducting transmon qubits in the QB context, giving promising results for the scalability of superconducting transmon qubits as QB. Our study paves the way forward to implementing quantum batteries for energy management in quantum technologies, a near-term future application of quantum batteries.

Superconducting circuits in cryogenic environments form an excellent material platform for the realization and study of quantum systems.
In this thesis, we continue the exploration of novel types of circuit elements which expand the circuit quantum electrodynamics toolbox to enable exotic, and potentially better circuit implementations. To this end, we combine the study of condensed matter systems and circuit quantum electrodynamics in what is called hybrid cQED experiments to arrive at the implementation of gate-tunable kinetic inductances for superconducting circuits. This discovery shed new light on the physics of gate-tunable kinetic inductances and enabled the observation of emergent phenomena in gate-tunable metamaterials, in particular the phase transition in a bosonic Su-Schrieffer-Heeger chain. Moreover, as gate-tunable kinetic inductances became available we realized tunable resonators and parametric amplifiers for enhanced control and readout of superconducting circuits.@en

Superconducting parametric amplifiers have been developed for fast and high
fidelity single shot readout of superconducting qubits. The nonliniarity re-
quired for those amplifiers is either based on various types of Josephson
junctions or high kinetic inductance materials. The Andersen Lab currently
develops a novel type of superconducting parametric amplifiers based on
superconducting-semiconducting hybrid nanowires, which will allow for in-
situ tuning of the amplifier characteristics with a gate voltage.
To prepare for the required performance tests of nanowire-based para-
metric amplifiers, we characterize a commercially available travelling wave
parametric amplifier in terms of 5 figures of merit: gain, bandwidth, satu-
ration power, noise temperature and quantum efficiency. We find a state of
the art amplifier performances, but also detect several hardware problems
in the measurement setup, which must be solved prior to further test. The
method implemented here can be generalized to the characterization of all
types superconducting parametric amplifiers.

Resonators are useful structures due to their simplicity in modeling, design, fabrication and measurement. They can be measured over a wide range of frequencies, power and temperatures, making them convenient for many experiments. Recently, superconducting resonators started being used to investigate microscopic phenomena which require applied magnetic fields of the order of 1T, such as Majorana physics. For this kind of applications it is important that resonators maintain high quality factors in the presence of magnetic fields. A suitable candidate easy to fabricate, resilient to applied fields, and simple capacitive coupling is the lumped element resonator. Such a type of resonator has already been used for some experiments that require magnetic fields, but a systematic study on the resonator’s optimal geometry is yet to be undertaken. The aim of this thesis is to investigate the role of lumped element resonator geometry in its quality factor. That is how to optimize the resonator’s design for enhanced performance of the resonator even in the presence of applied magnetic fields.