Protected qubits based on superconducting circuit topology

We propose a formalism that allows to determine whether an arbitrary superconducting circuit can act as a protected qubit. We do that by analyzing the phase-space topology of the studied circuit. The Hamiltonian of a superconducting circuit is a function of charge and phase variables. Instead of treating the space of n phase variables describing the circuit as a real vector space Rⁿ, we treat the phase space as a more complex manifold whose topology is determined by charge quantization in the superconducting circuit. This small change in approaching the Schrodinger equation has far-reaching consequences in terms of understanding topologically protected subspaces. Our approach provides a generalization for the stabilizer formalism. Most importantly, we show how it can be used to systematically search for new protected qubit designs.