Network-Based Quantum Computing: an efficient design framework for many-small-node distributed fault-tolerant quantum computing

TL;DR

This paper introduces Network-Based Quantum Computing (NBQC), a framework for distributed fault-tolerant quantum computing using many small, low-qubit-count nodes connected by slow quantum links. NBQC hides communication latency by circulating algorithmic qubits in ring networks and by deploying a strict-sense non-blocking switching fabric, yielding execution times near the algorithmic baseline $D T_{local}$ with manageable node overhead. It presents two designs—circuit-agnostic NBQC and circuit-specific NBQC—and provides an optimization workflow (NBQC construction, Clos-network optimization, bottleneck identification, and configuration updates) to adapt the network to resource limits. Numerical results show NBQC can outperform circuit-based and measurement-based DFQCs in the right regimes, offering a tunable trade-off between execution time and node count and demonstrating significant gains when access patterns are leveraged.

Abstract

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.

Figures (23)

• Figure 1: Design classification of DFTQC according to the number of nodes and the number of qubits per node. The left regime, distributed QEC, does not require integration technologies but demands quantum communication that is faster than the syndrome measurement cycle and has error rates lower than the code threshold, which is challenging for current technology. The right regime, few-large-node DFTQC or single-node FTQC, would be fast and simple, but its integration is challenging. In the middle regime, many-small-node DFTQC can be implemented with slow quantum communication and modest integration technology. Still, it might suffer from the execution time penalty due to massive communication. This paper focuses on the middle regime.
• Figure 2: An example implementation of fault-tolerant nodes with $n_{\rm node}=1$ and $d=3$. Each node contains a single data code block (blue cell), three sets of entanglement distillers, and ancillary qubits for local logical operations. Each communication code block (green cell) has a quantum channel to that in other nodes, and can prepare logical entangled states with low fidelity. They can be distilled using buffer cells (pink cell) to distill high-fidelity entanglement. Ancillary cells (gray cell) are used for performing logical $H$ and $S$ gates on data block fowler2018lowbeverland2022assessingbrown2017poking and local two-qubit gates to consume distilled entanglement or entanglement swapping. If each code block is implemented with the surface code, it corresponds to a 2D array of physical qubits, as shown in the bottom left. Here, blue and brown squares correspond to $X$ and $Z$ stabilizer measurements and circles to data qubits. Communication blocks have additional qubits that are physically connected to the other. See Sec. \ref{['sec:discussion']} for more general situations.
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• Figure 6: The achievable design space with CB-DFTQC, MB-DFTQC, and NBQC. The proposed method, NBQC, provides fast and resource-efficient designs compared to the existing approaches, and offers the tunability between execution time and node count.