Tunable coupler for superconducting Xmon qubits: Perturbative nonlinear model

TL;DR

This paper analyzes a tunable coupler design for superconducting qubits, showing how junction nonlinearity affects qubit interactions and providing a perturbative model to predict these effects.

Contribution

It introduces a perturbative nonlinear model for the coupler, quantifying the impact of junction nonlinearity on qubit-qubit interactions in superconducting circuits.

Findings

Nonlinearity suppresses transverse XX coupling by about 15%.

Nonlinearity induces a small diagonal ZZ coupling.

Coupler junction nonlinearity effects are negligible in the studied regime.

Abstract

We study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits [Y. Chen et al., arXiv:1402.7367]. The coupler circuit uses a single flux-biased Josephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse XX coupling from that obtained in the harmonic approximation by about 15%. The second is to induce a small diagonal ZZ coupling. The effects of the coupler junction nonlinearity are negligible in the parameter regime considered.