Tunable inductive coupling of superconducting qubits in the strongly nonlinear regime

TL;DR

This paper develops a non-perturbative theoretical framework for tunable, nonlinear inductive coupling of superconducting qubits, revealing complex interactions beyond linear models, with practical implications for quantum computing.

Contribution

It derives a general, non-perturbative interaction model for superconducting qubits coupled via nonlinear Josephson elements, including classical and quantum effects.

Findings

The interaction includes non-stoquastic and many-body terms.

The theory is applicable to any superconducting qubit type.

Numerical case study confirms the model's validity.

Abstract

For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper we derive the general interaction mediated by such a circuit under the Born-Oppenheimer Approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is non-perturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant departures from previous, linear theories for the inter-qubit coupling, including non-stoquastic and many-body interactions. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type. We conclude with a numerical investigation of our theory using a case study of two coupled flux qubits, and in particular study the regime of validity of the Born-Oppenheimer Approximation.