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arXiv:2510.18652

Measurement-Based Fault-Tolerant Quantum Computation on High-Connectivity Devices: A Resource-Efficient Approach toward Early FTQC

Yohei Ibe, Yutaka Hirano, Yasuo Ozu, Toru Kawakubo, Keisuke Fujii

Published Oct 21, 2025• 0 citations
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Abstract

We propose a measurement-based fault-tolerant quantum computing (MB-FTQC) architecture for high-connectivity platforms, targeting early-FTQC devices with thousands to tens of thousands of physical qubits. Unlike earlier teleportation-based architectures that rely on code concatenation for scalability, MB-FTQC operates in a zero-concatenation regime with compact fixed-distance codes, keeping the qubit overhead within reach of such devices. MB-FTQC combines offline-verified logical resource states with Knill's error-correcting teleportation, allowing each online step to use single-round syndrome extraction and independent lookup-table decoding. Under circuit-level depolarizing noise, we study a Steane-code implementation with partially fault-tolerant analog $R_Z(θ)$ rotations and a Golay-code implementation with higher-order zero-level distillation for fault-tolerant $T$-state preparation. At a physical error rate of $10^{-4}$, our estimates give a megaquop-scale equivalent $T$-count of $1.89\times10^{6}$ for the Steane implementation and a gigaquop-scale characteristic $T$-count of $1.87\times10^{9}$ for the Golay implementation. With sufficient parallel resource supply, MB-FTQC achieves a short online critical path, while resource estimates including verification failures and retries show competitive spacetime costs. These results show that compact, fixed-distance codes can support fault-tolerant computation at substantial scales in the early-FTQC regime, without code concatenation.

DOI
10.48550/arxiv.2510.18652

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Abstract The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice other factors. Here, we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates 10 −10 and 10 −24 by more than 90% and 96%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.5% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms. This can be remedied by protecting quantum information with a quantum error-correcting code, where the logical information of an algorithmic qubit is spread across multiple physical qubits. Individual quantum errors are then located and corrected by the fault-tolerant measurement of multi-qubit stabilizer operators (parity checks). Unfortunately, error correction and fault tolerance both impose large demands on the qubit overhead: hundreds to thousands of physical qubits per logical qubit. We reduce the spacetime cost of fault tolerance by redesigning key building blocks of an error-corrected quantum computer. First, we develop a combinatorial proof with flag fault tolerance that exponentially reduces the extra qubits needed to measure a stabilizer of any size, while tolerating one fault. We leverage these proofs to then design state preparation circuits for the Steane and Golay codes with 100% yield. Next, we improve error correction on a planar layout by showing that a distance-four code encoding six logical qubits protects information as well as the distance-five surface code, using one-tenth as many physical qubits. Finally, we optimize the time overhead of logical gates in surface code quantum computers by protecting measurement results with a classical code, cutting computation time by a factor of two to six. Our hardware-agnostic optimizations of fault tolerance overheads thus suggest new routes to advance the timeline of error-free quantum computing.