Quantum computers promise to solve certain problems such as quantum chemistry simulations much more efficiently than their classical counterparts. Although it is still unclear what material system will ultimately host large-scale quantum computers, solid-state systems are promising candidates due to their inherent scalability and advanced fabrication techniques that can be adapted from comparable technologies. Crucially, a future quantum computer will depend on the quality of its most fundamental building block, the quantum bit, or qubit. Qubits, although ideally insensitive to potential noise, are very susceptible to slight changes in their environment. Therefore, they do not only make the building block for quantum computers, but are also precise sensors. One of the most studied solid-state implementations of a qubit is the transmon, a weakly anharmonic oscillator based on superconducting capacitive and nonlinear inductive elements. Typically, Al-AlOx-Al superconductor-insulator-superconductor Josephson junctions are used for the latter. The interaction of the transmon with the control circuitry, typically superconducting resonators, is described by circuit quantum electrodynamics. In this PhD thesis, a more recently demonstrated type of qubit is further developed and studied in detail using circuit quantum electrodynamics. In these qubits, the Josephson element of the transmon is replaced with indium arsenide nanowires, forming a superconductor-normal metalsuperconductor junction. In addition to the standard flux tunability, these qubits can also be voltage tuned. Due to the compatibility of all the materials used with an applied magnetic field, this type of qubit is a good candidate to be used as a precise and accurate sensor in a magnetic field. The goal of this work is to introduce the in-plane magnetic field as a new tuning knob to the toolbox of circuit quantum electrodynamics. Advances in material science, especially the epitaxial growth of an aluminum shell directly on the indium arsenide nanowire, have enabled the fabrication of nanowire transmons with state-of-the-art coherence. An understanding of their workings in a zero-field environment is important before applying a magnetic field. Thus, we characterize the noise these qubits are subject to (Chapter 4) and find a strong coupling of charge two-level systems to their Josephson energy next to the expected weakly coupled flux and voltage noise. Applying a magnetic field reveals that coherence in these qubits can be observed up to 70 mT, substantially above the superconducting gap of bulk aluminum (Chapter 5). Effects limiting the performance include the thick and fully covering aluminum shell, and the alignment and stability of the magnetic field. The use of different nanowires, the installation of a persistent-current vector solenoid and additional magnetic shielding then enables the operation of voltage- and flux-tunable devices in a magnetic field (Chapter 6). This constitutes a good starting point for circuit quantum electrodynamics experiments in a magnetic field, such as the investigation of the microscopic origin of flux-noise.@en

We present an experimental study of flux- and gate-tunable nanowire transmons with state-of-the-art relaxation time allowing quantitative extraction of flux and charge noise coupling to the Josephson energy. We evidence coherence sweet spots for charge, tuned by voltage on a proximal side gate, where first order sensitivity to switching two-level systems and background 1/f noise is minimized. Next, we investigate the evolution of a nanowire transmon in a parallel magnetic field up to 70 mT, the upper bound set by the closing of the induced gap. Several features observed in the field dependence of qubit energy relaxation and dephasing times are not fully understood. Using nanowires with a thinner, partially covering Al shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation and other applications.

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We present a tuneup protocol for qubit gates with tenfold speedup over traditional methods reliant on qubit initialization by energy relaxation. This speedup is achieved by constructing a cost function for Nelder-Mead optimization from real-time correlation of nondemolition measurements interleaving gate operations without pause. Applying the protocol on a transmon qubit achieves 0.999 average Clifford fidelity in one minute, as independently verified using randomized benchmarking and gate-set tomography. The adjustable sensitivity of the cost function allows the detection of fractional changes in the gate error with a nearly constant signal-to-noise ratio. The restless concept demonstrated can be readily extended to the tuneup of two-qubit gates and measurement operations.

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The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of 80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.

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