In fault-tolerant quantum computing, a large number of physical qubits are required to construct a single logical qubit, and a single quantum node may be able to hold only a small number of logical qubits. In such a case, the idea of distributed fault-tolerant quantum computing (DFTQC) is important to demonstrate large-scale quantum computation using small-scale nodes. However, the design of distributed systems on small-scale nodes, where each node can store only one or a few logical qubits for computation, has not been explored well yet. In this paper, we propose network-based quantum computation (NBQC) to efficiently realize distributed fault-tolerant quantum computation using many small-scale nodes. A key idea of NBQC is to let computational data continuously move throughout the network while maintaining the connectivity to other nodes. We numerically show that, for practical benchmark tasks, our method achieves shorter execution times than circuit-based strategies and more node-efficient constructions than measurement-based quantum computing. Also, if we are allowed to specialize the network to the structure of quantum programs, such as peak access frequencies, the number of nodes can be significantly reduced. Thus, our methods provide a foundation in designing DFTQC architecture exploiting the redundancy of many small fault-tolerant nodes.

翻译：在容错量子计算中，构建单个逻辑量子比特需要大量物理量子比特，而单个量子节点可能仅能容纳少量逻辑量子比特。在此情况下，分布式容错量子计算（DFTQC）的理念对于利用小型节点实现大规模量子计算至关重要。然而，针对每个节点仅能存储一个或少数逻辑量子比特进行计算的小型节点分布式系统设计，目前尚未得到充分探索。本文提出基于网络的量子计算（NBQC）方法，以高效实现利用多小型节点的分布式容错量子计算。NBQC的核心思想是让计算数据在网络中持续流动，同时保持与其他节点的连接性。数值模拟表明，对于实际基准任务，我们的方法相较于基于线路的策略具有更短执行时间，较之基于测量的量子计算则具备更高的节点利用效率。此外，若允许根据量子程序结构（如峰值访问频率）定制网络拓扑，节点数量可显著减少。因此，我们的方法为利用多小型容错节点冗余性设计DFTQC架构奠定了理论基础。