  The increasingly complex quantum electronic circuits with a number of coupled
quantum degrees of freedom will become intractable to be simulated on classical
computers, and requires quantum computers for an efficient simulation. In turn,
it will be a central concept in quantum-aided design for next-generation
quantum processors. Here, we demonstrate variational quantum eigensolvers to
simulate superconducting quantum circuits with varying parameters covering a
plasmon-transition regime, which reveals an advanced post-transmon qubit,
"plasmonium". We fabricate this new qubit and demonstrate that it exhibits not
only high single- and two-qubit gate fidelities (99.85(1)% and 99.58(3)%,
respectively), but also a shrinking (by 60%) physical size and larger (by 50%)
anharmonicity than the transmon, which can bring a number of advantages for
scaling up multi-qubit devices. Our work opens the way to designing advanced
quantum processors using existing quantum computing resources.
