Symmetry considerations are key towards our understanding of the fundamental laws of Nature. The presence of a symmetry implies that a physical system is invariant under specific transformationsand this invariance may have deep consequences. For instance, symmetry arguments state that a system will remain in its initial state if incentives to actions are equally balanced. Here, we apply this principle to a chain of qubits and show that it is possible to engineer the symmetries of its Hamiltonian in order to keep quantum information intrinsically protected from both relaxation and decoherence. We show that the coherence properties of this system are strongly enhanced relative to those of its individual components. Such a qubit chain can be realized using a simple architecture consisting of a relatively small number of superconducting Josephson junctions.
The quasi-degenerate ground state manifold of the anisotropic Ising spin model can encode quantum information, but its degree of protection against local perturbations is known to beonly partial. We explain how the coupling between the two ground states can be used to observe signatures of Majorana zero modes in a small controlled chain of qubits. We argue that the protection against certain local perturbations persists across a range of parameters even away from the ideal point. Remarkably, when additional non-local interactions are considered the system enters a phase where the ground states are fully protected against all local field perturbations.
Combining superconducting qubits with mesoscopic devices that carry topological states of matter may lead to compact and improved qubit devices with properties useful for fault-tolerantquantum computation. Recently, a charge qubit device based on a topological superconductor circuit has been introduced where signatures of Majorana fermions could be detected spectroscopically in the transmon regime. This device stores quantum information in coherent superpositions of fermion parity states originating from the Majorana fermions, generating a highly isolated qubit whose coherence time could be greatly enhanced. We extended the conventional semi-classical method and obtained analytical derivations for strong transmon-photon coupling. The analytical challenge is rendered tractable via a formalism based on the WKB method that allows to extract the energy eigenstates of the qubit and its dipole matrix elements. Using this formalism, we study the effect of the Majorana fermions on the quantum electrodynamics of the device embedded within an optical cavity and develop protocols to initialise, control and measure the parity states. We show that, remarkably, the parity eigenvalue can be detected via dispersive shifts of the optical cavity in the strong coupling regime and its state can be coherently manipulated via a second order sideband transition.
We analyse the transmon regime Hamiltonian of a Cooper-Pair-Box where the superconducting phase difference is coupled to the zero energy parity states that arise from Majorana quasi-particles.We investigate the level structure and properties of the transmon qubit in this regime where even a small coupling causes hybridization of different transmon-parity states without compromising the suppression of charge dispersion. We show that the microwave photon-qubit coupling is sensitive to the gate bias and all the energy scales of the Hamiltonian. As well as a probe for topological-superconductor excitations, we propose that this type of device could be used to realise a high coherence tunable four-level system in the superconducting circuits architecture.