A new type of superconducting qubit: How the transmon thwarts the $T_2$ problem

Superconducting qubits have long been dogged by small energy relaxation ($T_1$) and dephasing times ($T_2$). Here we propose a new type of superconducting qubit that we call the ``transmon.'' This device consists of a Cooper pair box shunted by a large capacitance. The two quantities crucial to the operating the transmon as a qubit are a) energy level anharmonicity and b) charge noise sensitivity. Sufficient anharmonicity is required to prevent transitions out of the qubit two-level system. Low sensitivity is desired so that fluctuations of the gate charge do not appreciably change the qubit transition frequency. Decreasing (increasing) the Josephson energy to charging energy ratio ($E_J$/$E_C$) of the transmon raises (reduces) anharmonicity and charge noise sensitivity. By operating the transmon in a radically different parameter regime $10^1 < E_J/E_C \ll 10^3$, the qubit becomes exponentially more stable to charge fluctuations compared to the Cooper pair box, yet it retains enough anharmonicity for fast qubit operations. For large enough $E_J/E_C$, dephasing due to charge noise becomes completely negligible so that greatly enhanced $T_2$ times should be achievable.