Eigenspectra are the set of energy levels and eigenstates of the qubit Hamiltonian. For a transmon, the lowest two energy levels define the computational qubit; higher levels represent leakage states.

from scqubits import Transmon
 
transmon = Transmon(EJ=15.0, EC=0.3, ncut=30)
 
# Eigenvalues (energies)
evals = transmon.eigenvals(n=10)  # First 10 levels
print(evals)
 
# Eigenvectors (states)
evecs = transmon.eigenvecs(n=5)
 
# Energy differences (transition frequencies)
f_01 = evals[1] - evals[0]  # Qubit frequency
f_12 = evals[2] - evals[1]  # One-photon transition to |2⟩
print(f"f_01 = {f_01:.4f} GHz")
print(f"f_12 = {f_12:.4f} GHz")

The spectrum determines gate frequencies, pulse design, and leakage errors. Transmons have decreasing level spacing (nonlinear)—useful for selective control.

Anharmonicity $\alpha = f_{12} - f_{01}$: the nonlinearity. Large $\alpha$ enables fast, selective qubit operations.

Leakage levels: levels above $|1\rangle$ that can be accidentally excited during gates.

Understanding the full spectrum is essential for pulse design, multi-qubit gate engineering, and error analysis.