Self-Shunted Superconducting Flux Qubit

We proposed and theoretically investigated the self-shunted superconducting flux qubits (SSFQs) with relatively large Josephson junctions with the diameter over
$\text{1}\; \mu \text{m}$
. Because of the large self-capacitance of several 10 fF in the junctions, the large shunt capacitor with dimensions of several 100
$ \mu \text{m}$
of the conventional capacitively shunted flux quantum bits (qubits) can be eliminated, resulting in significant reduction of the footprint. We systematically calculated the SSFQ performances, such as the anharmonicity, and investigated their dependences on the circuit parameters. As a result, it was shown that the SSFQs have the large anharmonicity of 400–2000 MHz for the reasonable parameters, such as the large junction area of around 1
$ \mu \text{m}^{2}$
and the small critical current density of around 10
$\text{A/cm}^{2}$
. Furthermore, we derived and estimated the relative relaxation time of the SSFQs due to the charge and flux noises. As a result, we found that the high anharmonicity over 800 MHz could be achieved without degrading the relaxation time from that of the high-coherence flux qubits. The SSFQs offer the new choice of the highly scalable qubits, which achieve both the small footprint and high anharmonicity.