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Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…

Quantum Physics · Physics 2023-07-26 Adam Siegel , Armands Strikis , Thomas Flatters , Simon Benjamin

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…

Quantum Physics · Physics 2026-04-10 Andi Gu , J. Pablo Bonilla Ataides , Mikhail D. Lukin , Susanne F. Yelin

Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…

We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be…

Quantum Physics · Physics 2022-06-07 Yongsoo Hwang

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

Quantum Physics · Physics 2015-04-08 Keisuke Fujii

Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…

Quantum Physics · Physics 2026-01-27 Takeshi Kakizaki

Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant…

Quantum Physics · Physics 2026-05-26 Lorenzo Valentini , Diego Forlivesi , Marco Chiani

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into…

Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge…

Quantum Physics · Physics 2025-11-26 Pei Zeng , Guo Zheng , Qian Xu , Liang Jiang

Spin qubits in semiconductor structures bring the promise of large-scale 2D integration, with the possibility to incorporate the control electronics on the same chip. In order to perform error correction on this platform, the characteristic…

Quantum Physics · Physics 2024-07-10 Bence Hetényi , James R. Wootton

Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…

Quantum Physics · Physics 2024-08-28 Yutaro Akahoshi , Kazunori Maruyama , Hirotaka Oshima , Shintaro Sato , Keisuke Fujii

We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in…

Quantum Physics · Physics 2025-07-29 Jacob S. Nelson , Andrew J. Landahl , Andrew D. Baczewski

The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…

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…

Quantum Physics · Physics 2017-04-11 Shota Nagayama

We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…

Quantum Physics · Physics 2026-04-14 Guo Zhang , Yuanye Zhu , Ying Li

Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach…

Quantum Physics · Physics 2023-03-10 Héctor Bombín , Chris Dawson , Ye-Hua Liu , Naomi Nickerson , Fernando Pastawski , Sam Roberts

Modular architectures offer a scalable path toward fault-tolerant quantum computing by interconnecting smaller quantum processing units (QPUs) provided that high-rate, fault-tolerant interfaces can be realized across modules. We present a…

Quantum Physics · Physics 2026-05-05 Frederik K. Marqversen , Gefen Baranes , Maxim Sirotin , Johannes Borregaard

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against the dominant error source, excitation loss, in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation…

Quantum Physics · Physics 2022-10-25 Qian Xu , Guo Zheng , Yu-Xin Wang , Peter Zoller , Aashish A. Clerk , Liang Jiang

Fault-tolerant modular quantum computing requires stabilizer measurements across the modules in a quantum network. For this, entangled states of high quality and rate must be distributed. Currently, two main types of entanglement…

Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing…

Quantum Physics · Physics 2026-04-07 Nitish Kumar Chandra , David Tipper , Reza Nejabati , Eneet Kaur , Kaushik P. Seshadreesan