Abstract Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.
Abstract Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.
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.
In quantum information science and technology (QIST), the superposition of states is pivotal. Current qubits, formed by superposing two pure states, are foundational in QIST but are susceptible to decoherence, causing loss of superposed states. Addressing this, we introduced an "elastic bit" using the Hertz-type nonlinearity of elastic beads under external driving. These beads exhibit phase-dependent nonlinear vibrations, leading to coherent superpositions of energy states in linear vibration modes. The resulting amplitudes span a two-dimensional Hilbert space, with time allowing parametric spanning. We showcased the Hadamard gate, translating one state superposition to another through a unitary transformation. Remarkably, these elastic bits operate at room temperature and resist decoherence, making them apt for intermediate-scale quantum analogue computing. They offer solutions for challenges in supercomputing for artificial intelligence and autonomous vehicle data processing.
Abstract The stable operation of quantum computers will rely on error correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many physical qubits, but can also be realized using a single higher-dimensional quantum system, such as a harmonic oscillator1–3. In such a system, a powerful encoding has been devised based on periodically spaced superpositions of position eigenstates4–6. Various proposals have been made for realizing approximations to such states, but these have thus far remained out of reach7–11. Here we demonstrate such an encoded qubit using a superposition of displaced squeezed states of the harmonic motion of a single trapped 40Ca+ ion, controlling and measuring the mechanical oscillator through coupling to an ancillary internal-state qubit12. We prepare and reconstruct logical states with an average squared fidelity of 87.3 ± 0.7 per cent. Also, we demonstrate a universal logical single-qubit gate set, which we analyse using process tomography. For Pauli gates we reach process fidelities of about 97 per cent, whereas for continuous rotations we use gate teleportation and achieve fidelities of approximately 89 per cent. This control method opens a route for exploring continuous variable error correction as well as hybrid quantum information schemes using both discrete and continuous variables13. The code states also have direct applications in quantum sensing, allowing simultaneous measurement of small displacements in both position and momentum14, 15.
Abstract. We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator. This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schrödinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schrödinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schrödinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner. ar
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al. (2023), we present and implement a detailed quantum circuit construction for simulating one-dimensional spring–mass systems. Our approach incorporates key quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification, to realize the unitary time-evolution operator associated with simulating classical oscillators dynamics. In the uniform mass–spring setting, our circuit construction requires a gate complexity ofO(log22Nlog2(1/ε)), where N is the number of oscillators and$\varepsilon isthetargetaccuracyoftheapproximation.Formoregeneral,heterogeneousmass–springsystems,thetotalgatecomplexityis\mathcal {O}\bigl (N\log _{2} N\,\log _{2}(1/\varepsilon )\bigr ).Bothsettingsrequire\mathcal {O}(\log _{2} N)$qubits. Numerical simulations agree with classical solvers across all tested configurations, indicating that this circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.
We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator. This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schrödinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schrödinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schrödinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow one to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.