Encoding and Node Choices in Transversal Fault-Tolerant Distributed Quantum Computations: An Initial Study

2026-09-29

AI Summary

This study addresses the challenge of balancing entanglement resource consumption against logical error rates in distributed quantum computing by proposing a joint optimization strategy for bivariate bicycle (BB) codes and node selection. Through systematic analysis of how different BB codes affect non-local CNOT and global gate performance, combined with transversal fault-tolerant operations and distributed entanglement theory, this work demonstrates that merely minimizing ebit consumption is suboptimal and establishes the critical role of high-distance codes in suppressing logical error rates. Experimental results show that the [[120,8,12]] code supports eight concurrent logical GCZ operations, confirming the decisive impact of code selection on system performance. These findings offer a new paradigm for distributed fault-tolerant quantum computing.

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 encoding for the logical qubits, if the goal is to reduce the logical error rate of the distributed computation; for example, one should also consider encodings with a larger distance, which using more physical qubits can provide. We consider distributed, or non-local, CNOTs and computation of the global gate (GCZ) over distributed logical qubits as examples. The choice of encoding enables particular concurrent operations; e.g., we show that a transversal physical GCZ on a self-dual $[[120,8,12]] BB$ code can realize eight concurrent logical GCZ operations after accounting for the logical permutation induced by transversal Hadamard.

Problem

• Distributed Quantum Computing
• Fault-Tolerant
• Bivariate-Bicycle Codes
• Logical Error Rate
• Transversal Gates

Innovation

• Bivariate-Bicycle codes
• Distributed quantum computation
• Fault-tolerant
• Transversal gates
• Logical error rate