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I will discuss two types of protected qubits that decouple logical states from the environment by encoding them in a parity of a large number. The first type, the so-called charge-pairing qubit, represents a chain of two Josephson elements characterized by the π periodicity of the phase dependence of their Josephson energy E_J cos(2φ) (the so-called Josephson rhombi ). The second type, the flux-pairing qubit, consists of a 4π periodic Josephson element (a Cooper pair box with the charge e on the central island) shunted by a superinductor . The lowest-energy quantum states of the charge-pairing qubit are encoded in the parity of Cooper pairs on a superconducting island flanked by the Josephson rhombi. The flux-pairing qubit encodes its quantum states in the parity of magnetic flux quanta in a superconducting loop. The design of these devices enforces, respectively, charge- and flux-pairing, prohibits the mixing of lowest-energy quantum states, and protects the qubits from both the decay and dephasing. We have fabricated the prototypes of these qubits and studied the low-energy excitations in these devices [3,4] For the charge-pairing devices, we observed a 100-fold increase of the decay time T1 (up to 100 s) in comparison with the unprotected state of the same qubit .
1. S. Gladchenko, D. Olaya, E. Dupont-Ferrier, B. Douçot, L.B. Ioffe, and M.E. Gershenson. Superconducting Nanocircuits for Topologically Protected Qubits. Nature Physics 5, 48-53 (2009).
2. M.T. Bell, I.A. Sadovskyy, L.B. Ioffe, A.Yu. Kitaev, and M.E. Gershenson. Quantum Superinductor with Tunable Non-Linearity. Phys. Rev. Lett. 109, 137003 (2012).
3. M.T. Bell, J. Paramanandam, L.B. Ioffe, and M.E. Gershenson. Protected Josephson Rhombus Chains. Phys. Rev. Lett. 112, 167001 1-5 (2014).
4. M.T. Bell, W. Zhang, L.B. Ioffe, and M.E. Gershenson. Spectroscopic Evidence of the Aharonov-Casher Effect in a Cooper Pair Box. Phys. Rev. Lett. 116, 107002 (2016).