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

Abstract

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 wavefunction. In the other the junction is added in parallel, which gives rise to an extended phase variable, continuous wavefunctions and a rich energy level structure due to the loop topology. While the corresponding rf-SQUID Hamiltonian was introduced as a quadratic, quasi-1D 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 quasi-charge qubit with strongly enhanced zero point phase fluctuations and a heavily suppressed flux dispersion. The use of a geometric inductor results in high precision of the inductive and capacitive energy as guaranteed by top-down lithography -a key ingredient for intrinsically protected superconducting qubits. The geometric fluxonium also exhibits a large magnetic dipole, which renders it an interesting new candidate for quantum sensing applications.

Bound states in the continuum in a fluxonium qutrit

“…The characteristic energies of the fluxonium are the junction's Josephson energy E J , the charging energy introduced by the capacitance E C = e 2 /2C, and the inductive energy introduced by the inductance E L = ( /2e) 2 /L = Φ 2 0 /2. The main difference between this and other inductively shunted Josephson junction devices lies precisely in the relation between these parameters, which satisfy E L E J and 1 E J /E C [30]. The heavy fluxonium is realized approximately for E J /E C > 5 [29].…”

Scalable High-Performance Fluxonium Quantum Processor

“…For E L , if the superinductor is constructed from an array consisting of N = 100 junctions [49,75,154], independent fluctuations of individual junctions would reduce the fluctuation in E L by √ N times, or δE L /E L ∼ 0.2% if each junction fluctuates by 2%. In addition, geometric superinductors have recently been demonstrated to have variation as low as 0.2% as well [83]. This also corresponds to a frequency dispersion σ f 10 MHz.…”

“…They are typically constructed based on the phenomenon of kinetic inductance, with experimental realizations including arrays of Josephson junctions [49,75], superconducting nanowires [76][77][78], or disordered superconductors such as granular aluminum [79][80][81]. Recently, geometric superinductors have also been successfully fabricated and characterized [82,83].…”