Their work reveals this code transmits a logical qubit more efficiently than transmission-unaware encodings by accounting for signal loss during transmission. Over continental distances, the researchers found the cost-optimal repeater density is about an order of magnitude lower than a recent benchmark at comparable transmission rates. They extend the framework to a system where joint decoding allows for distributed quantum computation with a decoder-free client.

Asymmetry-Aided Repeaters Enable Continental Quantum Networks

A rectangular Bacon-Shor subsystem code improves the efficiency of logical qubit transmission over long distances by directly addressing photon loss in quantum repeater networks. This approach contrasts with conventional designs where the transmission layer and computation are treated as separate components, and instead recognizes a measurement-based quantum repeater as a two-dimensional code structured along the transmission axis. The resulting asymmetry concentrates channel loss on the transmission sector while preserving the fidelity of locally measured qubits, a key advantage for continental-scale networks.

This structural matching of code to network characteristics yields a demonstrably more efficient transmission of logical qubits than transmission-unaware encodings. Over continental distances, the cost-optimal repeater density is about an order of magnitude lower than that of a recent [[48,6,8]] benchmark at comparable transmission rate, and roughly half that of a symmetric code of equal size.

The framework extends to a central-to-client round trip in which a code-level, distance-preserving code switch joins the transmission legs to the client’s computation, and joint decoding of the heterogeneous syndrome record at the central node lets distributed quantum computation proceed with a decoder-free client. The researchers observed that the repeater protocol functions as a measurement-based quantum error correction process, allowing transmission and computation to be viewed within a unified framework.

This integrated approach considers an outbound transmission, edge computation and return transmission as a single, decoded record. “We do not advocate a fixed pairing of a Bacon–Shor transmission code with a surface-code computation,” the authors state, emphasizing that the core principle is structural.

Bacon-Shor Code Structure in Measurement-Based Quantum Repeaters

This approach recognizes that measurement-based quantum repeaters function as two-dimensional codes layered along the transmission path, concentrating channel loss on transmitted sectors while preserving locally measured qubits. The framework developed extends beyond simple transmission, integrating it with computation within a unified measurement-based system.

This difference in spacing is not a result of assuming perfectly reliable syndromes, but rather a direct consequence of the code’s structure and its adaptation to the transmission channel’s characteristics. The researchers state, emphasizing the fundamental role of code design in achieving these gains.

Decoder-Free Client Architecture for Distributed Quantum Computation

This architecture allows for a central node to manage error correction for a remote client, eliminating the need for a decoder at the client site and streamlining the process for lightweight or distant stations. The ability to defer global error correction to a central location represents a substantial simplification for remote computational units. Joint decoding of the combined syndrome record at the central node is key; the entire heterogeneous record is decoded once, centrally, allowing the client to execute prescribed operations and forward only the measurement outcomes.

This approach allows for a modular design where computation occurs at the edge of the network while error correction is centralized, offering flexibility in system architecture. The researchers state. This code transmits logical qubits more efficiently than those designed without considering transmission loss, a critical factor over continental distances.

By concentrating loss on the transmission sector, the code minimizes errors in the locally measured qubits, improving overall performance. The researchers note that a client need not run the global quantum error correction decoder, instead executing prescribed preparations, measurements and logical operations, and forwarding the syndrome record to the central node. This approach allows for a trade-off. A client could incorporate the loss and errors of its incoming leg into a local decode, exchanging the decoder-free client for a lighter, localized one.

The design choice of where to run the decode is itself a benefit of this architecture, offering adaptability based on computational needs. The team’s work demonstrates that this unified code-design perspective, treating both transmission and computation within the same measurement-based repeater, offers a significant advantage over traditional, separate designs. The researchers emphasize that the locality of distributed computation opens up new possibilities for system design and optimization.

One remaining assumption is a noiseless interface map, but the core framework presents a pathway toward more efficient and scalable quantum networks. The researchers state, “All global error correction is deferred to the center, a substantial simplification for a remote or lightweight station.”

Local vs. Transmitted Qubit Protection in Repeater Layers

This structural asymmetry, previously overlooked in bare 2D codes, forms the basis for improved performance when the code is foliated along the transmission axis, allowing for a more efficient allocation of protective coding distance. The team’s work demonstrates that matching a code’s distance to this asymmetry yields significant gains in long-distance quantum communication. The researchers quantified this asymmetry by considering distinct erasure rates for transmitted and locally prepared layers, where the transmitted layers experience a higher loss rate due to fiber transmission.

Every syndrome qubit generated and measured locally only experiences the local erasure rate, a convention adopted to provide a consistent comparison with surface code performance. Evaluating performance at a repeater efficiency of 0.9, comparisons between symmetric and asymmetric Bacon-Shor codes reveal substantial differences in cost-optimal repeater density. Specifically, the team analyzed four equal-pair codes: the symmetric BS(7×7) and BS(9×9), alongside their asymmetric counterparts BS(15×3) and BS(27×3). Results indicate that the cost-optimal effective transmission rate is notably higher for the asymmetric codes, and correspondingly, the cost-optimal repeater density is significantly lower.

Loss Tolerance and Erasure Correction in Photonic Repeaters

The approach uses the fact that photon loss, when heralded, manifests as erasure at known locations, a characteristic exploited to enhance code performance. Labels X and Z within the code refer to the two CSS sectors of the construction, distinguishing them from physical Pauli error channels, and the analysis focuses on per-qubit erasure probabilities seen by these sectors.

This improvement is not merely theoretical; the design guide exploits a loss bias analogous to biased-erasure error correction, and extends beyond transmission to encompass a computation round trip. The Bacon-Shor/surface-code interface is treated as noiseless in the transport simulation, a simplification justified by fault-tolerant injection schedules, though a full circuit-level Monte Carlo simulation would remove this remaining idealization. The transmission analysis focuses on heralded erasure as the dominant photonic error, excluding unheralded Pauli errors which would reinstate a finite threshold determined by the code distances, (d_Z,d_X) = (m,n).

👉 More information
🗞 Asymmetry-aided measurement-based quantum repeaters and distributed quantum computing with a decoder-free client
✍️ Wooyeong Song, Sungyeon Kook, Wonhyuk Lee and IlKwon Sohn (Quantum Network Research Center, Korea Institute of Science and Technology Information (KISTI), Daejeon 34141, Republic of Korea)
🧠 ArXiv: https://arxiv.org/abs/2607.11238v1

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