Non-Trivial Topological Majorana Architectures: Mobius and Trefoil Band Topologies evaluated by Signal to Noise Ratio and Coherence time mesuarements

Topological quantum computing is expected to be less sensitive to noise because information is stored in global states rather than local features. To examine whether different device topologies show measurable differences, we study three geometries with distinct topological invariants: a Mobius strip, a loop, and a trefoil knot, which have been proposed in electronic-structure settings. From quantum capacitance measurements, we extract power versus frequency spectra and fit Lorentzian line shapes to obtain the linewidth, amplitude, signal-to-noise ratio, and coherence time. The signal-to-noise ratio quantifies the ratio of the parity measurement signal to background noise and serves as an indicator of readout quality, while the coherence time characterizes the timescale for decoherence of the quantum state. Across all three topologies, coherence times are similar, with no clear dependence on geometry. In contrast, the signal-to-noise ratio differs in the regime E0 = 10 micro-eV and Z = -1, following the ordering Trefoil, Mobius, and Loop. These results provide a reference point for future experiments aimed at separating genuine topological effects from device-level parameters.