Relationship between a superconducting qubit and an atom In the literature on quantum computing, I commonly hear the assertion that a superconducting conducting circuits have the same properties as an atom, and thus behave like artificial atoms. Below we have a three parallel elements, a capacitor, an inductor, and a Josephson junction (that's $I_c$), which together form a superconducting circuit. Apparently, the non-linearity of the Josephson junctions is pivotal in mimicking the atomic system.

from
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Can someone please explain how these two systems are related?
**Edit: This question might not be specific enough for those of you who are not totally familiar with the relevant literature . Please tell what more you need to know if I'll try to fill it the gaps.
 A: Briefly, an ideal qubit is a two level quantum system which can be arbitrarily addressed and manipulated. The similarity between atoms and superconducting qubits is that in certain regimes they can each be treated as an addressable two level system. I'll discuss an atom first.
Atom: An atom has a broad range of electronic states available to it. However, if light is used to address a particular transition with energy difference $\hbar \omega_a$, it is possible (in certain regimes) to ignore all other energy levels and only consider the two levels which are linked by the transition. So the two levels are two different electronic atomic states and the addressability comes from driving transitions between the two levels using light. Sometimes we us lasers and optical transitions and other times we can use RF or microwave frequencies to address transitions.
Superconducting qubit: Here is the basic gist of a superconducting qubit. As you have identified the superconducting qubit creates and LRC circuit. We know from classical physics that LRC circuits have a resonance frequency which corresponds to current flowing back and forth in the circuit. Quantum mechanically we can think of this flow as being a quantum harmonic oscillator. We know from basic quantum mechanics that a harmonic oscillator has an infinite ladder of equally spaced energy levels with spacing $\hbar \omega_0$. Say the resonator begins in the ground state. We could drive it at energy $\hbar \omega_0$ to drive it to the first excited state. However, this is not a two level system because light which is resonant for the $0\rightarrow 1$ transition is also resonant to the $1\rightarrow2$ transition so we would be driving the resonator to a whole ladder of resonator states. This is where the nonlinearity comes in. The nonlinearity of the josephson junction has the effect of making the harmonic oscillator levels NOT equally spaced. This means that our $\hbar \omega_0$ drive is only resonant with the $0\rightarrow1$ transition and (in certain regimes) we can neglect all other energy levels. Typically the superconducting qubit is addressed with a microwave drive.
In summary, atoms and superconducting qubits are related by the fact that in certain regimes they can both be treated as addressable two level systems. i.e. they can both be used as qubits.
