# Two-level quantum circuit?

• This is related to my previous question:

Hamiltonian of a quantum circuit including a diode?

• The current most promising candidate for quantum computing are superconducting circuits, Transmon for example. One problem with Transmon, an anharmonic oscillator, is the leakage to higher energy levels when trying to drive it with short microwave pulses. As shorter pulses have larger bandwidth.

• I wonder if there exists quantum circuits that are two-level? If not, what is the fundamental reason that hinders their existence?

• I forgot to mention it in my answer to your previous question, but a Josephson junction is a good example of the type of the Hamiltonian that I suggested - with a non-linear potential. – Vadim Sep 18 at 9:23
• @Vadim . Thanks, Josephson junctions are exactly what are used in Transmons. The $\cos \hat{ \varphi }$ potential of the Josephson junctions locally looks like $\hat{ \varphi }^2$ of an inductor, making them anharmonic oscillators. The reason why I asked about diode comes from intuition: they have two states of on/off. Thanks to your previous answer I am now investigating the eigen-energies of the Hamiltonian with $\hat{V} = e^{\hat{\varphi}} -\hat{\varphi}$, which does not look like $\hat{ \varphi }^2$. Hopefully I get a better spectrum than that of the Transmon. – ruiqi ding Sep 18 at 9:47
• The above comment is invalid, due to the first comment of the first answer here: physics.stackexchange.com/questions/580433/… – ruiqi ding Sep 18 at 15:15