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arXiv:2610.20670

Mechanical trisqueezing in circuit quantum acoustodynamics with SNAIL devices

Yi-Zhou Bu, Matteo Fadel, Kai Xu, Heng Fan

quant-phSubmitted Oct 14, 2026• Announced Oct 15, 2026• 0 citations
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Abstract

Continuous-variable quantum information processing with mechanical oscillators requires a uni- versal gate set, including a genuine non-Gaussian evolution. While circuit quantum acoustodynamics (cQAD) experiments have realized bilinear and quartic (four-wave mixing) operations by coupling mechanical modes to transmon qubits, the intrinsic Kerr nonlinearity of these devices precludes access to odd-order effective Hamiltonians such as trisqueezing. Here we propose a cQAD architec- ture in which a mechanical mode, hosted in a high-overtone bulk acoustic-wave resonator (HBAR), is coupled to a superconducting nonlinear asymmetric inductive element (SNAIL). By combining the cubic nonlinearity of the SNAIL with parametric flux driving, we engineer a three-wave mixing interaction that generates trisqueezed mechanical states, producing the characteristic triangular, star-shaped Wigner function with negative regions indicative of non-Gaussianity. We derive the effective trisqueezing Hamiltonian from the full circuit model, identify the drive frequencies and flux modulation required to isolate the desired interaction from competing terms, and quantify the achievable coupling strengths for parameters compatible with current fabrication capabilities. Our results establish a hardware-efficient route to non-Gaussian resource generation in mechanical quantum systems, extending the toolbox of cQAD toward universal continuous-variable quantum computation and enhanced quantum-limited sensing.

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Mechanical resonators are emerging as a powerful platform for quantum information science, offering compactness, long coherence times, and scalability. In this thesis, we explore a circuit quantum acoustodynamics (cQAD) device based on integrating high-overtone bulk acoustic resonators (HBARs) with superconducting transmon qubits. This architecture harnesses the dense mode structure and high quality factors of HBARs alongside the fast control and high-fidelity readout of superconducting qubits. We demonstrate essential building blocks for phonon-based quantum operations, including direct measurements of phonon number and parity, as well as Wigner tomography of nonclassical states. We also realize Schrödinger cat states in a mechanical resonator with an effective mass of 16.2 micrograms and investigate their decoherence dynamics. Additionally, we demonstrate the creation and coherent control of a mechanical qubit enabled by strong single-phonon anharmonicity. Building on these capabilities, we introduce the concept of Acoustic Resonator-Based Quantum Circuits (ARQCs), where multiple phonon modes act as encoded qubits and a single transmon mediates interactions between them. This architecture supports compact, reconfigurable, and highly scalable quantum circuits capable of controlling hundreds of modes within a single device. Our experimental and simulation results position the cQAD platform as a compelling and versatile candidate for future quantum information processing technologies.
Three-wave mixing is a key process in superconducting quantum information processing, being involved in quantum-limited amplification and parametric coupling between superconducting cavities. These operations can be implemented by superconducting nonlinear asymmetric inductive element (SNAIL)-based devices that present a Kerr-free flux-bias point where unwanted parasitic effects, such as Stark shift, are suppressed. However, with a single flux-bias parameter, these circuits can only host one Kerr-free point, limiting the range of their applications. In this Letter, we demonstrate how to overcome this constraint by introducing the gradiometric SNAIL, a doubly flux biased superconducting circuit in which both effective inductance and Kerr coefficient can be independently tuned. Experimental data show the capability of the gradiometric SNAIL to suppress the Kerr effect in a three-wave mixing parametric amplifier over a continuum of flux bias points corresponding to a 1.7 GHz range of operating frequencies.
Collective dynamics in engineered quantum systems offer a unique and versatile platform for exploring how many-body correlations bridge microscopic entanglement and macroscopic behavior. In this work, we report collective Dicke dynamics of acoustic modes in a macroscopic high-overtone bulk acoustic resonator (HBAR). To achieve this, we engineer a hybrid quantum acoustodynamic system comprising an HBAR strongly coupled to a superconducting transmon qubit. The HBAR device is distinctive in the sense that its narrow mode spacing, together with enhanced qubit-mode coupling strength, gives rise to efficient coupling between the transmon and clusters of near-resonant modes. By harnessing the system properties, we observe collective dynamics involving clusters composed by two or three mechanical modes, where their non-resonant spectrum allows for the observation of the transition between the Dicke static regime to dynamically induced timed-Dicke one. The coherent collective behavior of the system is supported by time-domain measurements of the qubit's purity, indicating the quantum nature of the collective dynamics. Overall, our work establishes HBAR-based hybrid quantum system as a promising platform for exploring many-body collective dynamics in macroscopic mechanical systems.
Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.
Josephson parametric amplifiers are an important part of a modern superconducting quantum computing platform and squeezed quantum states generation devices. Traveling wave and impedance-matched parametric amplifiers provide broad bandwidth for high-fidelity single-shot readout of multiple qubit superconducting circuits. Here, we present a quantum-limited 3-wave-mixing parametric amplifier based on superconducting nonlinear asymmetric inductive elements (SNAILs), whose useful bandwidth is enhanced with an on-chip two-section impedance-matching circuit based on microstrip transmission lines. The amplifier dynamic range is increased using an array of 67 SNAILs with 268 Josephson junctions, forming a nonlinear quarter-wave resonator. Operating in a current-pumped mode, we experimentally demonstrate an average gain of 17 dB across 300 MHz bandwidth, along with an average saturation power of –100 dBm, which can go as high as −97 dBm with quantum-limited noise performance. Moreover, the amplifier can be fabricated using a simple technology with just one e-beam lithography step.
Circuit quantum acoustodynamics (cQAD) devices have a wide range of applications in quantum science, all of which depend crucially on the quantum coherence of the mechanical subsystem. In this context, high-overtone bulk acoustic-wave resonators (HBARs) are particularly promising, since they have shown very high quality factors with negligible dephasing. However, the introduction of piezoelectric films, which are necessary for coupling to a superconducting circuit, can lead to additional loss channels, such as surface scattering and two-level systems. Here, we study the acoustic dissipation of HBAR resonators in cQAD systems and find that the defect density of the piezoelectric material and its interface with the bulk are limiting factors for the coherence. We measure acoustic modes with phonon lifetimes up to 400 mu s and lifetime-limited coherence times approaching 1 ms in the quantum regime. When coupled to a superconducting qubit, this leads to a hybrid system with a large quantum coherence cooperativity of CT2 1/4 1.1 & times; 105. These results represent a new milestone for the performance of cQAD devices and offer concrete paths forward for further improvements.