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arXiv:2512.19896 · Physical Review Applied

Gate-Based Microwave Quantum Repeater Via Grid-State Encoding

Hany Khalifa, Matti Silveri

quant-phSubmitted Dec 22, 2025• Announced Dec 24, 2025• 0 citations• Revised Jul 6, 2026 (v2)
v1 · Dec 22, 2025v2 · Jul 6, 2026
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Abstract

In autonomous quantum error correction the lifetime of a logical bosonic qubit can be extended beyond its physical constituents without feedback measurements. Leveraging autonomous error correction, we propose a gate-based microwave quantum repeater (GBMQR) with encoded bosonic grid states. Each repeater station comprises a transmon and two bosonic resonators: one resonator serving as a stationary quantum memory utilizing autonomous error correction, and the other as an information bus for entanglement generation. Entanglement is generated sequentially through the successful absorption of a microwave photon wavepacket. This method enables deterministic entanglement generation, in contrast to a probabilistic mixing of two heralding signals on a balanced beamsplitter. Furthermore, our GBMQR employs an all-bosonic entanglement swapping Bell-state measurement. This is implemented via a bosonic controlled-Z gate and two separate X-basis projective homodyne measurements on the stationary stored codewords. Our approach circumvents mode-mismatch losses associated with routing and interfering of heralding modes on a beamsplitter, and confines losses to those arising from stationary storage. We evaluate the performance of the proposed quantum repeater by calculating its secret key rate under realistic lab environments. Moreover, we explicitly demonstrate that at stationary damping rate of $κ^{-1}_{\text{damp}}=$~\SI{40}{\milli\second}, GBMQR can achieve entanglement generation and swapping success probabilities approx.~$0.75$, and $0.58$ respectively, surpassing the hallmark success probability of $1/2$ set by ideal linear beamsplitter-based Bell-state measurements. The proposed device can be implemented using currently available superconducting microwave technology and is suited for secure chip-to-chip communication and distributed quantum computing.

DOI
10.1103/pg3m-jx2k

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In autonomous quantum error correction the lifetime of a logical bosonic qubit can be extended beyond its physical constituents without feedback measurements. Leveraging autonomous error correction, we propose a gate-based microwave quantum repeater (GBMQR) with encoded bosonic grid states. Each repeater station comprises a transmon and two bosonic resonators: one resonator serving as a stationary quantum memory utilizing autonomous error correction, and the other as an information bus for entanglement generation. Entanglement is generated sequentially through the successful absorption of a microwave photon wavepacket. This method enables deterministic entanglement generation, in contrast to a probabilistic mixing of two heralding signals on a balanced beamsplitter. Furthermore, our GBMQR employs an all-bosonic entanglement swapping Bell-state measurement. This is implemented via a bosonic controlled-Z gate and two separate X-basis projective homodyne measurements on the stationary stored codewords. Our approach circumvents mode-mismatch losses associated with routing and interfering of heralding modes on a beamsplitter, and confines losses to those arising from stationary storage. We evaluate the performance of the proposed quantum repeater by calculating its secret key rate under realistic lab environments. Moreover, we explicitly demonstrate that at stationary damping rate of κdamp−1=κ^{-1}_{\text{damp}}=κdamp−1​=\SI{40}{\milli\second}, GBMQR can achieve entanglement generation and swapping success probabilities approx.0.750.750.75, and 0.580.580.58 respectively, surpassing the hallmark success probability of 1/21/21/2 set by ideal linear beamsplitter-based Bell-state measurements. The proposed device can be implemented using currently available superconducting microwave technology and is suited for secure chip-to-chip communication and distributed quantum computing.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.
Long-distance quantum communication necessitates the use of quantum repeaters, which typically include highly coherent quantum memories. We provide a theoretical analysis of the secret key rates for a quantum repeater system incorporating bosonic error correction and memory components. Specifically, we focus on the application of Binomial codes for two repeater segments. Using these codes, our investigation aims to suppress memory loss errors that commonly affect systems such as atoms and microwave cavities, in contrast to dephasing errors in single-spin memories. We further discuss a physical implementation of such a quantum repeater comprising a microwave cavity and a superconducting transmon, capable of state engineering with high fidelities (>97%>97\%>97%) and logical Bell state measurements for successful entanglement swapping. As an alternative approach, we also discuss a realization in the all-optical domain.
To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available gate interactions be compatible with the code. A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code, for which a linear beamsplitter-like coupling between two bosonic modes is fault-tolerant, making this a key primitive for building larger systems. Here, using two motional modes of a trapped ion, we demonstrate the generation of entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter. We generate all four Bell states with an average fidelity of 69%, and subsequently demonstrate an extension of the entangled state lifetime through the use of quantum error correction. These results complete the set of Gaussian operations required for quantum computing with GKP codes and enable explorations of multi-mode bosonic encodings as well as fundamental tests of information channels.
Quantum repeaters that incorporate quantum error correction codes have been shown to be a promising alternative compared with the original quantum repeaters that rely upon probabilistic quantum error detection depending on classical communication over remote repeater stations. A particularly efficient way of encoding qubits into an error correction code is through bosonic codes where even a single oscillator mode serves as a sufficiently large, physical system. Here we consider the bosonic Gottesman-Kitaev-Preskill (GKP) code as a natural choice for a loss-correction-based quantum repeater. However, unlike existing treatments, we focus on the excitation loss that occurs in the local, stationary memory qubits as represented by, for instance, collective atomic spin modes. We analyze and assess the performance of such a GKP-based quantum repeater where, apart from the initial state generations and distributions, all operations can be performed via deterministic linear mode transformations, as opposed to other existing memory-based quantum repeater schemes.
Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.