Experimental realization of logical elastic bits as qubit analogues in a nonlinear oscillator

Nonlinear mechanical oscillators can emulate qubit analogue algebra by leveraging multiple harmonics of large‑amplitude vibrations. We realize a logical elastic bit—a room temperature mechanical analogue of a qubit—in a two‑mass oscillator joined by a conical spring whose graded stiffness generates a robust sequence of phase‑coherent harmonics. From time‑series velocity measurements, a Fourier–projection maps the response onto the complete space of in‑phase and out‑of‑phase eigenvectors. The resulting complex coefficients define a Bloch‑sphere representation in which classical superpositions are directly controllable. Moreover, we gain more control over the coefficients by pairing the Fourier harmonics in different orders. When the paired Fourier components share a frequency, the coefficients are independent of time, producing tunable states that can serve as phase-defined memory. Pairing distinct harmonics introduces a beat frequency that drives deterministic precession of the Bloch vector, realizing single‑bit rotations (e.g., Pauli‑X and Hadamard analogues) without the need of additional external input, with time as the gate clock. By splitting the spectrum into blocks, a single resonator can host several elastic bits at once. The Hilbert space grows with the number of blocks while the hardware stays the same, allowing scalable architectures that show classical non-separable correlations. A linear mass-spring model yields closed‑form eigenfrequencies and Bloch‑angle formulas that overlay measured trajectories across resonance and provide design rules for state initialization and gate timing. All operations occur at ambient conditions and require no feedback or cryogenics, establishing a simple, reproducible route to quantum‑inspired logic in macroscopic mechanics.