Geometric superinductance qubits: Controlling phase delocalization across a single Josephson junction

There are two elementary superconducting qubit types that derive directly from the quantum harmonic oscillator. In one, the inductor is replaced by a nonlinear Josephson junction to realize the widely used charge qubits with a compact phase variable and a discrete charge wave function. In the other, the junction is added in parallel, which gives rise to an extended phase variable, continuous wave functions, and a rich energy-level structure due to the loop topology. While the corresponding rf superconducting quantum interference device Hamiltonian was introduced as a quadratic quasi-one-dimensional potential approximation to describe the fluxonium qubit implemented with long Josephson-junction arrays, in this work we implement it directly using a linear superinductor formed by a single uninterrupted aluminum wire. We present a large variety of qubits, all stemming from the same circuit but with drastically different characteristic energy scales. This includes flux and fluxonium qubits but also the recently introduced quasicharge qubit with strongly enhanced zero-point phase fluctuations and a heavily suppressed flux dispersion. The use of a geometric inductor results in high reproducibility of the inductive energy as guaranteed by top-down lithography—a key ingredient for intrinsically protected superconducting qubits.