Tunable inductive coupling of superconducting qubits in the strongly nonlinear regime

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.

44 pages, 22 figures; minor revisions

References in corpus (8)

• Charge insensitive qubit design derived from the Cooper pair box
• Controllable coupling of superconducting flux qubits
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
• Switchable resonant coupling of flux qubits
• Mediated tunable coupling of flux qubits
• Superconducting Quantum Simulator for Topological Order and the Toric Code
• Tunable coupling of qubits: nonadiabatic corrections

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• On "Consistent Quantization of Nearly Singular Superconducting Circuits"
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