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arXiv:2610.18778

Deterministic and programmable generation of mechanical multipartite entangled states

Isabelle Franzen, Max-Emanuel Kern, Q. Rumman Rahman, Igor Kladarić, Stefano Marti, Yiwen Chu, Zhi-Yuan Wei, Matteo Fadel

quant-phSubmitted Oct 13, 2026• Announced Oct 14, 2026• 0 citations
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Abstract

Multimode mechanical resonators offer a large set of densely packed, long-lived bosonic modes within a single compact device, making them attractive for quantum simulation, quantum information processing, and quantum-enhanced sensing. Many such applications rely on multipartite entanglement, yet deterministic mechanical entanglement has so far been largely limited to pairs of modes. Here we demonstrate the deterministic and programmable preparation of multipartite entangled states among the phonon modes of a high-overtone bulk acoustic wave resonator coupled to a superconducting transmon qubit. By sequentially applying optimal-control-engineered isometries between the qubit and successive modes, we generate matrix product states of bond dimension two, including $W$, Greenberger-Horne-Zeilinger (GHZ), and cluster states. We fully characterize these states via quantum state tomography and certify genuine multipartite entanglement among up to four modes. We further demonstrate correlated-noise sensing by exploiting the complementary decoherence responses of the stored $W$ and GHZ states, isolating inter-mode phase correlations from local decoherence and placing quantitative bounds on collective dephasing. Our results establish a scalable approach to preparing multipartite entangled states in mechanical systems, with promising applications in multiparameter sensing and tests of quantum mechanics with massive objects.

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Multimode mechanical resonators offer a large set of densely packed, long-lived bosonic modes within a single compact device, making them attractive for quantum simulation, quantum information processing, and quantum-enhanced sensing. Many such applications rely on multipartite entanglement, yet deterministic mechanical entanglement has so far been largely limited to pairs of modes. Here we demonstrate the deterministic and programmable preparation of multipartite entangled states among the phonon modes of a high-overtone bulk acoustic wave resonator coupled to a superconducting transmon qubit. By sequentially applying optimal-control-engineered isometries between the qubit and successive modes, we generate matrix product states of bond dimension two, including WWW, Greenberger-Horne-Zeilinger (GHZ), and cluster states. We fully characterize these states via quantum state tomography and certify genuine multipartite entanglement among up to four modes. We further demonstrate correlated-noise sensing by exploiting the complementary decoherence responses of the stored WWW and GHZ states, isolating inter-mode phase correlations from local decoherence and placing quantitative bounds on collective dephasing. Our results establish a scalable approach to preparing multipartite entangled states in mechanical systems, with promising applications in multiparameter sensing and tests of quantum mechanics with massive objects.
Generating complex multimode entanglement is a central goal of quantum information science. However, scalable creation of genuine multipartite entanglement is challenging as it requires excellent control and efficient state verification. We report the generation and transfer of genuine multimode entanglement across two multimode acoustic resonators. We prepare genuine multipartite entangled states involving two, four, and six modes across the resonators with respective fidelities of 0.912 ± 0.003, 0.790 ± 0.003, and 0.570 ± 0.001. We further demonstrate the transfer of two- and four-mode genuine entangled states between the resonators with fidelities of 0.785 ± 0.006 and 0.601 ± 0.006. This hardware-efficient and scalable architecture enables deterministic control and generation of complex multimode mechanical states. Our results push the boundary of quantum control in macroscopic mechanical systems, establishing a pathway toward large-scale mechanical quantum networks.
Fock states of the quantum harmonic oscillator are fundamental to quantum sensing and information processing, serving as key resources for exploiting bosonic degrees of freedom. Here, we prepare high Fock states in a high-overtone bulk acoustic wave resonator by coupling it to a superconducting qubit and applying microwave pulses designed using quantum optimal control. We characterize the experimentally realized states by employing a criterion for genuine quantum non-Gaussianity (QNG) designed to reveal multiphonon contributions. Although energy relaxation and decoherence limit the achievable fidelities, we demonstrate genuine QNG features compatible with a Fock state |6⟩, confirming that the prepared states cannot be generated through Gaussian operations on states with up to Fock state |5⟩ contributions. We further investigate the robustness of these QNG features to losses and their utility in sensing displacement amplitudes. In particular, we introduce a hierarchy based on the quantum Fisher information and show that, despite decoherence and measurement imperfections, the prepared states achieve a displacement sensitivity surpassing that of an ideal Fock state |3⟩. Our results have immediate applications in quantum sensing and simulations with high-overtone bulk acoustic wave resonator devices.
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.
In recent years, important progress has been made towards encoding and processing quantum information in the large Hilbert space of bosonic modes. Mechanical resonators have several practical advantages for this purpose, because they confine many high-quality-factor modes into a small volume and can be easily integrated with different quantum systems. However, it is challenging to create direct interactions between different mechanical modes that can be used to emulate quantum gates. Here we demonstrate an in situ tunable beamsplitter-type interaction between several mechanical modes of a high-overtone bulk acoustic-wave resonator. The engineered interaction is mediated by a parametrically driven superconducting transmon qubit, and we show that it can be tailored to couple pairs or triplets of phononic modes. Furthermore, we use this interaction to demonstrate the Hong-Ou-Mandel effect between phonons. Our results lay the foundations for using phononic systems as quantum memories and platforms for quantum simulations.
Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.
The development of quantum acoustics has enabled the cooling of mechanical objects to their quantum ground state, generation of mechanical Fock-states, and Schrödinger cat states. Such demonstrations have made mechanical resonators attractive candidates for quantum information processing, metrology, and macroscopic tests of quantum mechanics. However, generating large-amplitude phonon states in quantum acoustic systems has been elusive. In this work, a single superconducting qubit coupled to a high-overtone bulk acoustic resonator is used to generate a large phonon population in an acoustic mode of a high-overtone resonator. We observe extended ringdowns of the qubit, confirming the generation of a large amplitude phonon state, and also observe an upper threshold behavior, a consequence of phonon quenching predicted by our model. This work provides a key tool for generating arbitrary phonon states in circuit quantum acoustodynamics, which is important for fundamental and quantum information applications.