Towards curved-time quantum logic devices: photon-controlled electron teleportation on Gaussian acceleration platforms

Curved-time quantum systems provide a computational framework in which engineered local time-dilation fields, generated by Gaussian acceleration profiles (spatial envelope 𝑎(𝑥)), create discrete temporal eigenstates that operate as qubit analogs. Using curvature wells with 𝐴0 = 1.3, σ = 8, and γ = 1, we show that graphene nanoribbons and carbon-nanotube (CNT) rings support temporal confinement with well depths of 35 − 50meV and low-lying mode splitting of Δ𝐸 = 4.5− 6.2meV, corresponding to intrinsic teleportation periods of 𝑇tele ≈ 350 − 460fs. Time-dependent Schrödinger simulations reveal coherent electron transfer between curvature wells with > 95% probability transfer per cycle and effective tunneling velocities on the order of 105m/s, reproducing deterministic temporal-qubit π-rotations without electromagnetic gate fields. Together, these results establish curved-time quantum architectures as experimentally accessible platforms for ultrafast quantum logic, where information processing is encoded directly in engineered temporal geometry rather than external electromagnetic control. The combination of graphene/CNT transport, curvature-driven tunneling, and optically programmable temporal entanglement provides a pathway toward compact, high-speed, and photonics-assisted curved-time quantum processors.