Flux Dual Description of Noise-Insensitive Superconducting Qubits

Many superconducting qubits, such as transmons, are naturally described in terms of Cooper-pair charges hopping on and off of the nodes of the superconducting circuit. Others, such as flux qubits, are naturally described via superconducting vortices hopping in and out of the loops of the superconducting circuit. This talk describes a method to transform the Hamiltonian of a superconducting circuit from the Cooper-pair number basis to the dual vortex-number basis. In contrast to other methods that also accomplish this transformation, our method is non-perturbative and isospectral. It provides a useful framework to compare and evaluate the novel properties of qubits of the flux-qubit type such as nonstoquasticity and decreased sensitivity to environmental noise.