Nonlinear Transmons

Transmon qubits are typically capacitively coupled to resonators and the qubit-resonator coupling is well described by the Jaynes-Cummings Hamiltonian. But this model has some limitations. One of them is that higher levels of the transmon qubit can only be excited sequentially after exciting the lowest ones. This is usually regarded as an advantage, since for quantum computation purposes it is convenient to limit the Hilbert space to two states only and disregard higher states and their coupling to the resonator. But an extended coupling where we can selectively excite any transmon level can offer new possibilities for quantum information transmission and processing. This extended behavior can be accomplished by replacing the capacitor, which has an energy quadratic in the potential E(V)=C (V^2)/2with a “nonlinear capacitor”. This is an element com-posed of two parallel plates—very much like a capacitor—with carbon nanotubes between the plates. This results into an energy E(V)=C ((V^2+αV^4))⁄2,with α being a parameter that depends on the details of the nanostructure. The fabrication of such device is not a challenge, but a theoretical description of such a system as well as an analysis of its possible applications is still missing and will be researched in this project.