arXiv:2609.37210v1 Announce Type: cross Abstract: We compare and study different Bivariate-Bicycle (BB) encodings and node choices for distributed quantum operations such as transversal non-local CNOTs. We observe that while some encodings have more physical qubits requiring more ebits for a distributed computation, reducing ebit consumption alone might not be the best criterion for selecting an
Seng W. Loke’s study arXiv:2609.37210v1 (September 2026) investigates Bivariate-Bicycle (BB) encodings and node configurations for transversal fault-tolerant distributed quantum computing. The research compares using a single large code block versus multiple smaller blocks, analyzing the trade-offs between ebit consumption and logical error rates (LER).
Key findings include: Efficiency over Minimal Ebits: Selecting encodings based solely on minimizing ebit consumption is suboptimal; higher code distance and efficiency metrics ($kd^2/n$) often yield lower LERs despite higher resource costs. Performance Comparison: A single [[90,8,10]] BB block per node achieves significantly lower LERs than two [[36,4,6]] blocks, despite requiring more ebits (90 vs. 72). Concurrency: Specific self-dual BB codes, such as [[120,8,12]], enable eight concurrent logical GCZ operations via transversal physical gates. Optimization Framework: The paper proposes formulating encoding and node selection as a constrained optimization problem to minimize circuit LER, dependent on specific circuit and architecture constraints.
This paper presents an initial comparative study of Bivariate-Bicycle (BB) code encodings and node-selection choices in the context of distributed, fault-tolerant quantum computation. It focuses on operations that require non-local entanglement between separate quantum nodes, with transversal non-local CNOTs as a representative case. In such modular or distributed architectures, the choice of code parameters and the assignment of logical qubits to physical nodes affect how many long-range entangled pairs—ebits—are needed to implement a given logical operation.
A key observation is that encodings with more physical qubits per logical qubit can increase the number of ebits required for distributed operations, suggesting a direct resource tradeoff. However, the authors argue that minimizing ebit consumption alone is not necessarily the best selection criterion. The study points toward a broader cost model in which factors such as logical circuit depth, physical qubit overhead, error propagation, synchronization requirements, and architectural constraints may all influence the practical efficiency of a distributed fault-tolerant protocol.
This matters because distributed quantum computing is a promising route to scaling beyond single-device limits, but resource accounting for multi-node systems is more nuanced than in monolithic designs. By examining how BB code choices and node placement interact for non-local gates, the work provides early guidance for designing modular fault-tolerant architectures where the goal is not merely to reduce entanglement usage, but to optimize the full physical and logical resource footprint of distributed quantum computation.