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

TL;DR

This work addresses whether nontrivial band topology in Majorana-based qubits affects measurable performance metrics. It combines the Majorana–Quantum Dot coupling model with geometry-specific boundaries for three topologies (Mobius strip, loop, trefoil knot), computing flux-dependent quantum capacitance and extracting SNR and coherence time from Lorentzian fits to power spectra. Across most parameter sets, coherence time is topology-insensitive, while SNR shows topology-dependent variation only in the regime $E_0=10\,\mu\mathrm{eV}$ and $Z=-1$, with the Trefoil topology yielding the largest SNR; otherwise, SNR differences are muted. These results establish that topology can improve readout fidelity but does not inherently extend coherence, providing a baseline for distinguishing genuine topological effects from device-related parameters and guiding device design toward readout optimization rather than longer coherence times.

Abstract

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.

Figures (2)

• Figure 1: CQ signal as a function of $\phi$ for Closed Loop, $\text{M\"obius}$ Strip, and Trefoil topology
• Figure 2: Power as a function of frequency using a Discrete Fourier Transform of $C_Q$ Plot