Transversal Fanout for Fault Tolerant Distributed Quantum Computing: Analysis and Application

As quantum computing scales toward modular, distributed architectures, implementing multi-qubit gates across separate processing units becomes a primary bottleneck. This paper investigates a resource-efficient method for performing logical fanout operations—where one control qubit acts on multiple target qubits—in a fault-tolerant, distributed setting. The central question is whether transversal gate gadgets, which naturally preserve the structure of quantum error-correcting codes, can be leveraged to minimize the non-local communication overhead required for these operations.

The author utilizes Bivariate-Bicycle (BB) codes, a class of quantum low-density parity-check (qLDPC) codes, to construct distributed fanout circuits. Because logical CNOT operations in BB codes are transversal, the author demonstrates that logical fanout can be decomposed into a set of independent physical fanout operations across the code's coordinates. The study compares two primary distributed implementations: a sequential approach using distributed Bell pairs (CNOTs) and a concurrent approach using distributed GHZ states. The author performs a simulation study using the Stim library and the Tesseract decoder to evaluate the Logical Error Rate (LER) of these circuits under various physical error rates.

The simulation results indicate that the GHZ-based fanout implementation generally outperforms the sequential CNOT-based approach in terms of LER, particularly in the low-noise regime. Specifically, the "1-shot" GHZ approach, which treats the creation of the distributed GHZ state as a single logical step, provides the lowest error rates. The author further demonstrates that this transversal fanout technique can be applied to construct distributed global gates, such as the Global Controlled-Z (GCZ) gate, by exploiting the concurrency inherent in the transversal operations. The study confirms that these distributed circuits maintain the expected fault-tolerant distance of the underlying code.