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We have studied the low-energy excitations in a minimalistic protected Josephson circuit which contains two basic elements (rhombi) characterized by the $pi$ periodicity of the Josephson energy. Novel design of these elements, which reduces their sensitivity to the offset charge fluctuations, has been employed. We have observed that the life time $T_{1}$ of the first excited state of this quantum circuit in the protected regime is increased up to $70mu s$, a factor of $sim100$ longer than that in the unprotected state. The quality factor $omega_{01}T_{1}$ of this qubit exceeds $10^{6}$ . Our results are in agreement with theoretical expectations; they demonstrate the feasibility of symmetry protection in the rhombi-based qubits fabricated with existing technology.
We study coherent quantum phase-slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode s
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the norm
We present general symmetry arguments that show the appearance of doubly denerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its propertie
We propose a superconducting thermal memory device that exploits the thermal hysteresis in a flux-controlled, temperature-biased superconducting quantum-interference device (SQUID). This system reveals a flux-controllable temperature bistability, whi
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$pi$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of