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The generation of high-fidelity distributed multi-qubit entanglement is a challenging task for large-scale quantum communication and computational networks 1 – 4 . The deterministic entanglement of two remote qubits has recently been demonstrated with both photons 5 – 10 and phonons 11 . However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily owing to limited state-transfer fidelities. Here we report a quantum network comprising two superconducting quantum nodes connected by a one-metre-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the cable to one qubit in each node, we transfer quantum states between the nodes with a process fidelity of 0.911 ± 0.008. We also prepare a three-qubit Greenberger–Horne–Zeilinger (GHZ) state 12 – 14 in one node and deterministically transfer this state to the other node, with a transferred-state fidelity of 0.656 ± 0.014. We further use this system to deterministically generate a globally distributed two-node, six-qubit GHZ state with a state fidelity of 0.722 ± 0.021. The GHZ state fidelities are clearly above the threshold of 1/2 for genuine multipartite entanglement 15 , showing that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers 16 , 17 . High-fidelity deterministic quantum state transfer and multi-qubit entanglement are demonstrated in a quantum network comprising two superconducting quantum nodes one metre apart, with each node including three interconnected qubits.

One of the hallmarks of quantum physics is the generation of non-classical quantum states and superpositions, which has been demonstrated in several quantum systems, including ions, solid-state qubits and photons. However, only indirect demonstrations of non-classical states have been achieved in mechanical systems, despite the scientific appeal and technical utility of such a capability 1 , 2 , including in quantum sensing, computation and communication applications. This is due in part to the highly linear response of most mechanical systems, which makes quantum operations difficult, as well as their characteristically low frequencies, which hinder access to the quantum ground state 3 – 7 . Here we demonstrate full quantum control of the mechanical state of a macroscale mechanical resonator. We strongly couple a surface acoustic-wave 8 resonator to a superconducting qubit, using the qubit to control and measure quantum states in the mechanical resonator. We generate a non-classical superposition of the zero- and one-phonon Fock states and map this and other states using Wigner tomography 9 – 14 . Such precise, programmable quantum control is essential to a range of applications of surface acoustic waves in the quantum limit, including the coupling of disparate quantum systems 15 , 16 . A non-classical superposition of zero- and one-phonon mechanical Fock states is generated and measured by strongly coupling a surface acoustic-wave resonator to a superconducting qubit.

Mechanical systems have emerged as a compelling platform for applications in quantum information, leveraging advances in the control of phonons, the quanta of mechanical vibrations. Experiments have demonstrated the control and measurement of phonon states in mechanical resonators, and while dual-resonator entanglement has been demonstrated, more complex entangled states remain a challenge. Here, we demonstrate rapid multi-phonon entanglement generation and subsequent tomographic analysis, using a scalable platform comprising two surface acoustic wave resonators on separate substrates, each connected to a superconducting qubit. We synthesize a mechanical Bell state with a fidelity of F = 0.872 ± 0.002 , and a multi-phonon entangled N = 2 N00N state with a fidelity of F = 0.748 ± 0.008 . The compact, modular, and scalable platform we demonstrate will enable further advances in the quantum control of complex mechanical systems. Recent advancements have enabled quantum control and measurement of mechanical resonators. Here the authors demonstrate quantum entanglement between two mechanical resonators on separate substrates by sharing one and two quanta of energy, followed by quantum measurement of these entangled states.

Phonons, and in particular surface acoustic wave phonons, have been proposed as a means to coherently couple distant solid-state quantum systems. Individual phonons in a resonant structure can be controlled and detected by superconducting qubits, enabling the coherent generation and measurement of complex stationary phonon states. We report the deterministic emission and capture of itinerant surface acoustic wave phonons, enabling the quantum entanglement of two superconducting qubits. Using a 2-millimeter-long acoustic quantum communication channel, equivalent to a 500-nanosecond delay line, we demonstrate the emission and recapture of a phonon by one superconducting qubit, quantum state transfer between two superconducting qubits with a 67% efficiency, and, by partial transfer of a phonon, generation of an entangled Bell pair with a fidelity of 84%.

Quantum communication testbeds provide a useful resource for experimentally investigating a variety of communication protocols. Here we demonstrate a superconducting circuit testbed with bidirectional multi-photon state transfer capability using time-domain shaped wavepackets. The system we use to achieve this comprises two remote nodes, each including a tunable superconducting transmon qubit and a tunable microwave-frequency resonator, linked by a 2 m-long superconducting coplanar waveguide, which serves as a transmission line. We transfer both individual and superposition Fock states between the two remote nodes, and additionally show that this bidirectional state transfer can be done simultaneously, as well as used to entangle elements in the two nodes.

In the field of quantum computation and communication there is a compelling need for quantum-coherent frequency conversion between microwave electronics and infra-red optics. A promising platform for this is an optomechanical crystal resonator that uses simultaneous photonic and phononic crystals to create a co-localized cavity coupling an electromagnetic mode to an acoustic mode, which then via electromechanical interactions can undergo direct transduction to electronics. The majority of work in this area has been on one-dimensional nanobeam resonators which provide strong optomechanical couplings but, due to their geometry, suffer from an inability to dissipate heat produced by the laser pumping required for operation. Recently, a quasi-two-dimensional optomechanical crystal cavity was developed in silicon exhibiting similarly strong coupling with better thermalization, but at a mechanical frequency above optimal qubit operating frequencies. Here we adapt this design to gallium arsenide, a natural thin-film single-crystal piezoelectric that can incorporate electromechanical interactions, obtaining a mechanical resonant mode at f_m ~ 4.5 GHz ideal for superconducting qubits, and demonstrating optomechanical coupling g_om/(2pi) ~ 650 kHz.

In circuit quantum electrodynamics (QED), qubits are typically measured using dispersively-coupled readout resonators. Coupling between each readout resonator and its electrical environment however reduces the qubit lifetime via the Purcell effect. Inserting a Purcell filter counters this effect while maintaining high readout fidelity, but reduces measurement bandwidth and thus limits multiplexing readout capacity. In this letter, we develop and implement a multi-stage bandpass Purcell filter that yields better qubit protection while simultaneously increasing measurement bandwidth and multiplexed capacity. We report on the experimental performance of our transmission-line--based implementation of this approach, a flexible design that can easily be integrated with current scaled-up, long coherence time superconducting quantum processors.

Linear optical quantum computing provides a desirable approach to quantum computing, with a short list of required elements. The similarity between photons and phonons points to the interesting potential for linear mechanical quantum computing (LMQC), using phonons in place of photons. While single-phonon sources and detectors have been demonstrated, a phononic beamsplitter element remains an outstanding requirement. Here we demonstrate such an element, using two superconducting qubits to fully characterize a beamsplitter with single phonons. We further use the beamsplitter to demonstrate two-phonon interference, a requirement for two-qubit gates, completing the toolbox needed for LMQC. This advance brings linear quantum computing to a fully solid-state system, along with straightforward conversion between itinerant phonons and superconducting qubits.

High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel however degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these non-idealities, by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconducting quantum nodes connected by a moderately lossy, 1-meter long superconducting communication cable. We use a purification process to correct the dominant amplitude damping errors caused by transmission through the cable, with fractional increases in fidelity as large as \\(25\\%\\), achieved for higher damping errors. The best final fidelity the purification achieves is \\(94.09\\pm 0.98\\%\\). In addition, we use both dynamical decoupling and Rabi driving to protect the entangled states from local noise, increasing the effective qubit dephasing time by a factor of 4, from \\(3~\\rm \\mu s\\) to \\(12~\\rm\\mu s\\). These methods demonstrate the potential for the generation and preservation of very high-fidelity entanglement in a superconducting quantum communication network.

Phonon modes at microwave frequencies can be cooled to their quantum ground state using conventional cryogenic refrigeration, providing a convenient way to study and manipulate quantum states at the single phonon level. Phonons are of particular interest because mechanical deformations can mediate interactions with a wide range of different quantum systems, including solid-state defects, superconducting qubits, and optical photons when using optomechanically active constructs. Phonons, thus, hold promise for quantum-focused applications as diverse as sensing, information processing, and communication. In this thesis, we describe a piezoelectric quantum bulk acoustic resonator with a 4.88 GHz resonant frequency, which, at cryogenic temperatures, displays large electromechanical coupling strength combined with a high intrinsic mechanical quality factor Qi ∼ 4.3 * 104. Using a recently developed flip-chip technique, we couple this resonator to a superconducting qubit on a separate die and demonstrate the quantum control of the mechanics in the coupled system. The resonator lifetime at a single phonon level is measured, which yields a Qi ∼ 5.43 * 103. This lower quality factor at a single phonon level is likely due to the two-level system (TLS) defects contamination in the device. To test whether this dissipation comes from the TLS defects, a hole-burning technique is implemented to saturate those defects. As a result, the resonator quality factor is enhanced back to Qi ∼ 3 * 104, which demonstrates that TLS defects contribute the dissipation significantly in our device.