Collective modes in the fluxonium qubit

Abstract

Superconducting qubit designs vary in complexity from single-and few-junction systems, such as the transmon and flux qubits, to the many-junction fluxonium. Here, we consider the question of whether the many degrees of freedom in the fluxonium circuit can limit the qubit coherence time. Such a limitation is in principle possible, due to the interactions between the low-energy, highly anharmonic qubit mode and the higher-energy, weakly anharmonic collective modes. We show that so long as the coupling of the collective modes with the external electromagnetic environment is sufficiently weaker than the qubit-environment coupling, the qubit dephasing induced by the collective modes does not significantly contribute to decoherence. Therefore, the increased complexity of the fluxonium qubit does not constitute by itself a major obstacle for its use in quantum computation architectures.

High-Coherence Fluxonium Qubit

“…Because of the non-linearity of the plasma modes, occupation of one such mode by a single photon introduces a dispersive shift of about 0.1% of the qubit frequency. This shift is much larger than the qubit's natural linewidth [50]. Hence, in order for the qubit to have a coherence time T 2 , the average time for the absence of an out-of-equilibrium photon excitation in each mode must be longer than N × T 2 .…”

Nanowire Superinductance Fluxonium Qubit

“…In this regime, the presence of stray ground capacitance and the large kinetic inductance lower the frequencies of the self-resonant modes of the device. As is the case of long junction arrays [2], the multimode structure of the device needs to be taken into account to produce an accurate theoretical description [22,23].In this Letter, we demonstrate a fluxonium circuit integrating a NbTiN nanowire superinductance. We charac- * These authors contributed equally to this work.terize the effect of the nanowire modes on the qubit spectrum with a multimode circuit theory accounting for the distributed nature of the superinductance.…”

Inductively shunted transmon qubit with tunable transverse and longitudinal coupling

“…This has the advantage that the resulting transverse coupling [Eq. (33)] is flux-dependent and goes through zero at ϕ x = k π/2, which leads to pure longitudinal coupling. Transverse coupling terms caused by asymmetric inductances or capacitances would, however, be independent of the external flux.…”

“…With such a treatment, we are of course neglecting the dynamics of the internal degrees of freedom of the array [33,34]. This is justified as long as the energies of these degrees of freedom are far enough separated from the relevant energies of our system, that is, the frequencies of qubit and resonator.…”