Larger L and C Slower the Mode - Superconducting Qubits: LC Energy, Toy Josephson Coupling, and Readout Step by Step

Increasing both storage elements raises the LC product, so the reciprocal frequency-square ledger gets smaller and the ideal mode slows. The row arithmetic is exact only for the stated L and C values and the normalized oscillator model; actual qubit hardware adds tolerances, parasitic modes, dielectric loss, kinetic inductance shifts, and frequency measurement uncertainty.

Changing both storage elements changes the frequency square. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Larger storage elements raise the product

Using 2 henry and 2 farad gives product 4 square seconds.

2\ \text{H}\cdot 2\ \text{F}=4\ \text{s}^{2}

The frequency square becomes one fourth

The reciprocal of the product is 1/4 per square second, so the mode is slower.

\omega^{2}=\tfrac{1}{4}\ \text{s}^{-2}