Practical fault-tolerant quantum computation requires a large number of physical qubits, posing a major challenge for scaling up individual quantum processors. Distributed architectures offer a promising solution by interconnecting multiple processors through quantum networks. However, remote Bell-pair generation remains technically demanding, making it essential to assess computational performance under limited communication resources. In this work, we present a comprehensive resource analysis of distributed fault-tolerant quantum computation using superconducting processors connected by microwave or optical links. We show that even a single physical communication channel per node can substantially reduce the physical-qubit requirements per node under experimentally motivated, forward-looking microwave-link assumptions of a 1 MHz physical Bell-pair generation rate and 90% fidelity, although at the cost of a roughly tenfold increase in execution time. Conversely, reducing the execution-time overhead requires substantially greater communication resources, including higher Bell-pair fidelities and extensive multiplexing. These results demonstrate the potential feasibility of distributed fault-tolerant quantum computation with limited communication resources and provide a quantitative basis for balancing quantum-link performance, processor size, and execution time.
Practical fault-tolerant quantum computation requires a large number of physical qubits, posing a major challenge for scaling up individual quantum processors. Distributed architectures offer a promising solution by interconnecting multiple processors through quantum networks. However, remote Bell-pair generation remains technically demanding, making it essential to assess computational performance under limited communication resources. In this work, we present a comprehensive resource analysis of distributed fault-tolerant quantum computation using superconducting processors connected by microwave or optical links. We show that even a single physical communication channel per node can substantially reduce the physical-qubit requirements per node under experimentally motivated, forward-looking microwave-link assumptions of a 1 MHz physical Bell-pair generation rate and 90% fidelity, although at the cost of a roughly tenfold increase in execution time. Conversely, reducing the execution-time overhead requires substantially greater communication resources, including higher Bell-pair fidelities and extensive multiplexing. These results demonstrate the potential feasibility of distributed fault-tolerant quantum computation with limited communication resources and provide a quantitative basis for balancing quantum-link performance, processor size, and execution time.
The development of fault-tolerant quantum computers (FTQCs) is receiving increasing attention within the quantum computing community. Like conventional digital computers, FTQCs, which utilize error correction and millions of physical qubits, have the potential to address some of humanity’s grand challenges. However, accurate estimates of the tangible scale of future FTQCs, based on transparent assumptions, are uncommon. How many physical qubits are necessary to solve a practical problem intractable for classical hardware? What costs arise from distributing quantum computation across multiple machines? This paper presents an architectural model of a potential FTQC based on superconducting qubits, divided into discrete modules and interconnected via coherent links. We employ a resource-estimation framework and software tool to assess the physical resources required to execute specific quantum algorithms compiled into their graph-state form and arranged onto a modular superconducting hardware architecture. Our tool can predict the size, power consumption, and execution time of these algorithms based on explicit assumptions about the physical layout, thermal load, and modular connectivity of the system. We assess the resources needed for quantum computation examples that serve as building blocks of proposed applications, quantifying the architectural bottlenecks and trade-offs that remain to be addressed to deliver utility.
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.
Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum computing architecture, comprising small processors interconnected by quantum links, is emerging as a promising approach to fault-tolerant quantum computing. However, the requirements that the network must fulfill to enable distributed quantum computation remain largely unexplored. We consider an architecture tailored for qubits with nearest-neighbor physical connectivity, leveraging the surface code for error correction and enabling fault-tolerant operations through lattice surgery and magic state distillation. We propose measurement teleportation as a tool to extend lattice surgery techniques to qubits located on different computing units interconnected via Bell pairs. Through memory simulations, we build an error model for logical operations and deduce an end-to-end resource estimation of Shor’s algorithm over a minimalist distributed architecture. Concretely, for a characteristic physical gate error rate of 10 − 3 , a processor cycle time of 1 µs, factoring a 2048-bit RSA integer is shown to be possible with 379 computing processors, each made with 89 781 qubits, with negligible space and time overhead with respect to a monolithic approach without parallelization, if 70 Bell pairs are available per cycle time between each processor with a fidelity exceeding 98.1 % .
Fault tolerant quantum computation over distributed quantum computing (DQC) platforms requires careful evaluation of resource requirements and noise thresholds. As quantum hardware advances toward modular and networked architectures, various fault tolerant DQC schemes have been proposed, which can be broadly categorized into three architectural types. Type 1 architectures consist of small quantum nodes connected via Greenberger-Horne-Zeilinger (GHZ) states, enabling nonlocal stabilizer measurements. Type 2 architectures distribute a large error correcting code block across multiple modules, with most stabilizer measurements remaining local, except for a small subset at patch boundaries that are performed using nonlocal CNOT gates. Type 3 architectures assign code blocks to distinct modules and can perform fault tolerant operations such as transversal gates, lattice surgery, and teleportation to implement logical operations between code blocks. Using the planar surface code and toric code as representative examples, we analyze how the resource requirements, particularly the number of Bell pairs and the average number of generation attempts, scale with increasing code distance across different architectural designs. This analysis provides valuable insights for identifying architectures well suited to fault tolerant distributed quantum computation under near term hardware and resource constraints.
Building fault-tolerant quantum computers with large numbers of logical qubits requires both scalable hardware architectures and error-correcting codes that make efficient use of physical qubits. Photonic interconnects address both of these challenges by allowing the physical qubits to be distributed across multiple processors while providing the non-local connectivity necessary to implement resource-efficient codes such as high-rate quantum low-density parity-check (qLDPC) codes. A key requirement for realising this architecture is the ability to perform stabiliser measurements between remote processors, which has not previously been demonstrated experimentally. Here we report the first experimental demonstration of distributed quantum error detection and correction. We generate entanglement between network qubits in two separate trapped-ion processors and use it to perform remote syndrome measurements on data qubits. We first realise a distributed [[2, 1, 1]] repetition code, detecting phase-flip errors on a logical qubit encoded across the two modules in real time and suppressing logical errors. We then combine these mid-circuit syndrome measurements with real-time feedforward to actively correct arbitrary single-qubit Pauli errors on a distributed Bell state. These results provide an experimental foundation for quantum error correction (QEC) across modular quantum architectures.
The limited qubit resources of current quantum processing units (QPUs), together with their susceptibility to operational imperfections, environmental noise, and error propagation, not only degrade computational fidelity but also constrain the scalability required for utility-scale quantum computing. Consequently, the transition from monolithic architectures to distributed quantum computing (DQC), supported by distributed quantum error-correcting codes (QECCs), is emerging as a promising paradigm for large-scale fault-tolerant quantum computing (FTQC). This transition represents a full-stack challenge that requires coordinated advances in quantum architecture, fault-tolerant gate operations, and classical–quantum co-processing and control. In this paper, we review the theoretical foundations and practical realization of large-scale FTQC. We first explore major families of QECCs, including topological, qLDPC, subsystem, and dynamical codes, with emphasis on code construction, syndrome extraction, and decoding. We then review the implementation of fault-tolerant universal gate sets at the physical and logical levels, followed by entanglement generation, distribution, and purification for distributed architectures. Finally, we outline open challenges and future research directions in theory, architecture, and implementation, highlighting the role of distributed fault-tolerant designs in next-generation utility-scale quantum computing.