Space-Time Tradeoffs of Pauli-Based Computation in Distributed qLDPC Architectures

TL;DR

This paper analyzes the tradeoffs in distributed quantum computing architectures using Pauli-based computation, showing large qLDPC codes outperform surface codes in execution time.

Contribution

It demonstrates that Pauli-based computation with large qLDPC codes is practical and faster than surface codes in distributed quantum architectures at intermediate scales.

Findings

Large qLDPC code blocks outperform surface codes by up to an order of magnitude in execution time.

Moving qubit groups to free nodes reduces network operations and speeds up computation.

Pauli-based computation is a competitive and practical model for distributed quantum systems.

Abstract

Pauli-based computation (PBC) provides a universal framework for executing fault-tolerant quantum algorithms using Pauli measurements and magic states. In monolithic architectures, the serialized nature of PBC directly ties runtime to a circuit's T-gate count, making it slow on metrics like circuit depth. However, in distributed quantum computing (DQC), the primary bottleneck is remote Bell pair generation. We investigate the tradeoff between error-correcting code block size and execution time of PBC within the Q-Fly architecture at intermediate scale, limiting individual node capacities to reflect near-term constraints while supplying abundant network nodes to minimize routing and compilation effects. We find that large qLDPC code blocks outperform the surface code baseline in terms of execution time by up to an order of magnitude when evaluated against quantum optimization algorithms. By moving groups of qubits to free nodes to bypass the sequential bottleneck of PBC, the large-block architecture minimizes network operations and achieves faster overall execution. This demonstrates that PBC is a competitive model in the distributed regime, establishing it as a practical compilation baseline for qLDPC systems before invoking more efficient transversal or homological gates.