Fluxonium qubits with multiple degrees of freedom

According to Greek myths, Dionysus was born from the thigh of his father Zeus and promised to a great fate. He, the son of a mortal mother, was destined to become god of wine, festivities and frenzy. Physics too has a Dionysus, heir to the Nobel lineage of condensed matter, called to a bright quantum computing future and sometimes caught up in the media frenzy: the field of superconducting qubits. Like the god of madness and folly, qubits are unpredictable and difficult to control. Thus, generations of students and advisors have worked on designing, engineering and operating single-degree-of-freedom circuits, achieving high levels of accuracy in qubit manipulation and readout. Today, research builds upon these systems to add degrees of freedom, in particular in quantum processors and noise-protected qubits. This work fits within this line of research and aims to realize a protected qubit based on a proposed four-loop fluxonium circuit. In order to work as intended, the system first needs to trap and retain a persistent current equivalent to one flux quantum in the circuit, referred to as a fluxon. Second, it needs to be as insensitive as possible to the charge offset on its central island. ... mehrThese two requirements constitute the two challenges tackled in this thesis.

The first challenge is to trap and retain a fluxon in the circuit. To do this, we propose to cool down the device in a magnetic field corresponding to one flux quantum in its most external loop. This flux-locking technique is demonstrated on gradiometric fluxoniums, in which an aluminum ring retains the trapped fluxon indefinitely. On average, four out of five qubits are locked simultaneously in a single waveguide. By compensating the inductive asymmetry between the two loops of the design, we are able to lock the effective flux-bias within $\Phi_\mathrm{eff} = -3\times10^{-4} \,\Phi_0$ from the target, corresponding to only 15% degradation in coherence time $T_{2,\mathrm{E}}$ when operated in zero external field. Using such a gradiometric geometry for flux-tunable elements in quantum processors would reduce flux crosstalk and potentially eliminate the need for passive biasing.

The second challenge is the charge-offset noise arising from the central island in the design. To address it, we engineer charge-tunable fluxoniums in which the main junction is replaced by two junctions in series, separated by an island. In such a system, quasiparticles tunneling through either junction change the charge offset by one elementary charge $e$, a process called parity switching. By employing state-of-the-art techniques of infrared filtering and gap engineering, we increase the parity switching time to twenty seconds.
We also identify other phenomena, such as a parity saturation by microwave pumping, allowing us to prepare the qubit in odd or even parity with above 80% fidelity.
Finally, these devices can be used to uncover the coupling mechanism of qubits to long-lived two-level systems in their environment.

Overall, this thesis paves the way to studying multiple degrees of freedom, be it in multi-qubit processors or in a single superconducting circuit based on the fluxonium architecture. It highlights the phenomena that need to be understood and mitigated in order to translate protected qubit concepts into experimental reality.