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arXiv:1202.6588

A distributed architecture for scalable quantum computation with realistically noisy devices

Keisuke Fujii, Takashi Yamamoto, Masato Koashi, Nobuyuki Imoto

Published Feb 29, 2012• 15 citations
arXivHTMLPDF

Abstract

Tremendous efforts have been paid for realization of fault-tolerant quantum computation so far. However, preexisting fault-tolerant schemes assume that a lot of qubits live together in a single quantum system, which is incompatible with actual situations of experiment. Here we propose a novel architecture for practically scalable quantum computation, where quantum computation is distributed over small-size (four-qubit) local systems, which are connected by quantum channels. We show that the proposed architecture works even with the error probability 0.1% of local operations, which breaks through the consensus by one order of magnitude. Furthermore, the fidelity of quantum channels can be very low $\sim$ 0.7, which substantially relaxes the difficulty of scaling-up the architecture. All key elements and their accuracy required for the present architecture are within reach of current technology. The present architecture allows us to achieve efficient scaling of quantum computer, as has been achieved in today's classical computer.

DOI
10.48550/arxiv.1202.6588

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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.
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.
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Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation presents a new quantum computer architecture which takes into account imperfections, aimed to realize distributed computation by connecting quantum computers each of which consists of multiple quantum CPUs and memories. Quantum CPUs employ a quantum error correcting code which has faster logical gates and quantum memories employ a code which is superior in space resource requirements. This dissertation focuses on quantum error correcting codes, giving a practical, concrete method for tolerating static losses such as faulty devices for the surface code. Numerical simulation with practical assumptions showed that a yield of functional qubits of 90% is marginally capable of building large-scale systems, by culling the poorer 50% of lattices during post-fabrication testing. Yield 80% is not usable even when culling 90% of generated lattices. For internal connections in a quantum computer and for connections between quantum computers, this dissertation gives a fault-tolerant method that bridges heterogeneous quantum error correcting codes. Numerical simulation showed that the scheme, which discards any quantum state in which any error is detected, always achieves an adequate logical error rate regardless of physical error rates in exchange for increased resource consumption. This dissertation gives a new extension of the surface code suitable for memories. This code is shown to require fewer physical qubits to encode a logical qubit than conventional codes. This code achieves the reduction of 50% physical qubits per a logical qubit. Collectively, the elements to propose the distributed quantum computer architecture are brought together.
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 computing 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 article, we propose network-based quantum computing (NBQC) to efficiently realize distributed fault-tolerant quantum computing 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.