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All-photonic one-way quantum repeaters with measurement-based error correction

Daoheng Niu, Yuxuan Zhang, Alireza Shabani, Hassan Shapourian

Published Oct 21, 2023• 18 citations
Publisher

Abstract

Abstract Quantum repeater is the key technology enabler for long-distance quantum communication. To date, most of the existing quantum repeater protocols are designed based on specific quantum codes or graph states. In this paper, we propose a general framework for all-photonic one-way quantum repeaters based on the measurement-based error correction, which can be adapted to any Calderbank–Shor–Steane code including the recently discovered quantum low-density parity check (QLDPC) codes. We present a decoding scheme, where the error correction process is carried out at the destination based on the accumulated data from the measurements made across the network. This procedure not only outperforms the conventional protocols with independent repeaters but also simplifies the local quantum operations at repeaters. As an example, we numerically show that the [[48, 6, 8]] generalized bicycle code (as a small but efficient QLDPC code) has an equally good performance while reducing the resources by at least an order of magnitude.

DOI
10.1038/s41534-023-00775-9

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arXiv:2203.07979•Optica•Dec 21, 2021•26 citations
Abstract Quantum repeater is the key technology enabler for long-distance quantum communication. To date, most of the existing quantum repeater protocols are designed based on specific quantum codes or graph states. In this paper, we propose a general framework for all-photonic one-way quantum repeaters based on the measurement-based error correction, which can be adapted to any Calderbank–Shor–Steane code including the recently discovered quantum low-density parity check (QLDPC) codes. We present a decoding scheme, where the error correction process is carried out at the destination based on the accumulated data from the measurements made across the network. This procedure not only outperforms the conventional protocols with independent repeaters but also simplifies the local quantum operations at repeaters. As an example, we numerically show that the [[48, 6, 8]] generalized bicycle code (as a small but efficient QLDPC code) has an equally good performance while reducing the resources by at least an order of magnitude.
Quantum repeater is the key technology enabler for long-distance quantum communication. To date, most of the existing quantum repeater protocols are designed based on specific quantum codes or graph states. In this paper, we propose a general framework for all-photonic one-way quantum repeaters based on the measurement-based error correction, which can be adapted to any Calderbank-Shor-Steane codes including the recently discovered quantum low density parity check (QLDPC) codes. We present a novel decoding scheme, where the error correction process is carried out at the destination based on the accumulated data from the measurements made across the network. This procedure not only outperforms the conventional protocols with independent repeaters but also simplifies the local quantum operations at repeaters. As an example, we numerically show that the [[48,6,8]] generalized bicycle code (as a small but efficient QLDPC code) has an equally good performance while reducing the resources by at least an order of magnitude.
Measurement-based quantum repeaters employ entanglement distillation and swapping across links using locally prepared resource states of minimal size and local Bell measurements. In this Letter, we introduce a systematic protocol for measurement-based entanglement distillation and its application to repeaters that can leverage any stabilizer code. Given a code, we explicitly define the corresponding resource state and derive an error-recovery operation based on all Bell measurement outcomes. Our approach offers deeper insights into the impact of resource state noise on repeater performance while also providing strategies for efficient preparation and fault-tolerant preservation of resource states. As an application, we propose a measurement-based repeater protocol based on quantum low-density parity-check (QLDPC) codes, enabling constant-yield Bell state distribution over arbitrary distances. Numerical simulations identify a fault-tolerant threshold on the total physical error per repeater segment-including errors on resource states, remotely generated Bell states, and Bell measurements-and confirm that increasing the QLDPC code size further suppresses the logical error while maintaining a fixed encoding rate. This Letter establishes a scalable backbone for future global-scale fault-tolerant quantum networks.
Quantum low-density parity check (qLDPC) codes offer higher encoding rate than topological codes, e.g. surface codes, making them favourable for practical, fault-tolerant quantum computing with low overhead. These codes are particularly well-suited for fusion-based photonic implementations as this platform readily supports non-local connections. We propose an architecture specifically tailored to quantum emitters which can implement any Calderbank-Shor-Steane (CSS) qLDPC code. In this architecture, the photonic resource states are deterministically produced via quantum emitters and a conditional repeat-until-success strategy is incorporated to achieve high photon loss tolerance. We simulate small exemplary Bivariate Bicycle qLDPC codes and analyse the performance of our constructions under relevant physical noise mechanisms, including erasures due to fusion failure or photon loss, as well as Pauli errors. We obtain performances comparable with topological architectures though with significantly higher encoding rates.
The near-capacity performance of classical low-density parity check (LDPC) codes and their efficient iterative decoding makes quantum LDPC (QLPDC) codes a promising candidate for quantum error correction. In this paper, we present a comprehensive survey of QLDPC codes from the perspective of code design as well as in terms of their decoding algorithms. We also conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-four cycles. Our modified decoder outperforms the state-of-the-art decoders in terms of their word error rate performance, despite imposing a reduced decoding complexity. Finally, we intricately amalgamate our modified decoder with the classic uniformly reweighted belief propagation for the sake of achieving an improved performance.
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.
The all-photonic quantum repeater (APQR) is a promising repeater scheme to realize long-distance quantum communication. For a practical APQR, an indispensable requirement is the robustness of the repeater graph state (RGS) against photon loss. We propose a new loss-tolerant scheme by applying the generalized Shor code to RGS, which can be experimentally demonstrated with current technology. Experimentally, we first prepare and verify the nine-qubit Shor code. Then, by applying the generalized Shor code to APQR and preparing a simplified encoded RGS with the structure of 1 × 2 based on the Shor code state, the effectiveness of our loss-tolerant scheme and the loss tolerance of the encoded RGS are respectively verified. Our results make an essential step toward a practical APQR and enrich the research of quantum error correction code.