Classical Mechanical Qubit Analogues in a Nonlinear Elastic Oscillator

Nonlinear mechanical oscillators can replicate quantum qubit-like algebra through the interaction of multiple harmonics generated under large-amplitude vibrations. We experimentally demonstrate a logical elastic bit—a macroscopic, room-temperature analogue of a qubit—using a two-mass nonlinear oscillator. This configuration produces a stable sequence of phase-coherent harmonics whose amplitudes and phases are extracted from time-resolved velocity measurements. Fourier projection onto the orthogonal in-phase and out-of-phase eigenmodes maps the motion into a Bloch-sphere representation, where complex coefficients define controllable classical superpositions. Pairing harmonics of identical frequency yields stationary, phase-defined states functioning as memory elements, while detuned pairings generate beat frequencies that drive predictable Bloch-sphere precession, realizing Pauli-X and Hadamard-like rotations with time serving as the intrinsic gate clock. Partitioning the harmonic spectrum into multiple frequency blocks enables several elastic bits to coexist within a single resonator, enlarging the effective Hilbert space without additional components. A nonlinear mass–spring model reproduces the measured Bloch trajectories and provides closed-form design expressions for state preparation and gate timing. This approach establishes a scalable, room-temperature framework for quantum-inspired computation using purely classical mechanical systems.