Question

Why are Josephson junctions used in superconducting qubits instead of standard linear inductors?

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A superconducting qubit requires a quantum system with discrete energy levels that are non-equally spaced, a condition known as anharmonicity. A standard linear inductor combined with a capacitor forms a harmonic oscillator, which is a circuit where the energy levels are perfectly equally spaced, like the rungs of a ladder. In a harmonic oscillator, the transition frequency between any two adjacent levels is identical, making it impossible to isolate two specific levels to represent the 0 and 1 states of a qubit. A Josephson junction, which consists of two superconductors separated by a thin insulating barrier, acts as a non-linear inductor. This non-linearity arises because the current through the junction depends on the sine of the phase difference across it, rather than just the phase difference itself. This relationship introduces a non-quadratic term into the circuit potential energy, which effectively squashes or stretches the energy levels so they are no longer equally spaced. By making the system anharmonic, the Josephson junction allows the control signals to target only the transition between the ground state and the first excited state without accidentally exciting higher energy levels. Consequently, the Josephson junction is the essential component that turns a simple superconducting circuit into a tunable two-level quantum system capable of acting as a qubit.

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Why are Josephson junctions used in superconducting qubits instead of standard linear inductors?

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