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The quantum computing scheme described in Phys. Rev. Lett. 98, 190504 (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through…

Quantum Physics · Physics 2009-07-16 Austin G. Fowler , Kovid Goyal

Measurement-based quantum computation (MBQC) offers a promising paradigm for photonic quantum computing, but its implementation requires the generation of specific non-Gaussian resource states. While continuous-variable encodings such as…

Quantum Physics · Physics 2026-01-22 G. P. Teja , Radim Filip

Solving quantum molecular systems presents a significant challenge for classical computation. The advent of early fault-tolerant quantum computing (EFTQC) devices offers a promising avenue to address these challenges, leveraging advanced…

Quantum Physics · Physics 2025-11-10 Yukun Zhang , Xiaoming Zhang , Jinzhao Sun , Heng Lin , Yifei Huang , Dingshun Lv , Xiao Yuan

Blind Quantum Computation (BQC) is a delegation computing protocol that allows a client to utilize a remote quantum server to implement desired quantum computations while keeping her inputs, outputs, and algorithms private. However, qubit…

Quantum Physics · Physics 2023-03-07 Qiang Zhao , John C. S. Lui

We propose a scalable way to construct a 3D cluster state for fault-tolerant topological one-way computation (TOWC) even if the entangling two-qubit gates succeed with a small probability. It is shown that fault-tolerant TOWC can be…

Quantum Physics · Physics 2010-12-23 Keisuke Fujii , Yuuki Tokunaga

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…

Quantum Physics · Physics 2026-01-15 Soshun Naito , Yasunari Suzuki , Yuuki Tokunaga

High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…

Quantum Physics · Physics 2025-09-22 Naoyuki Kanomata , Hayato Goto

Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quantum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a…

Quantum Physics · Physics 2024-03-05 M. Schwetz , R. M. Noack

This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…

Quantum Physics · Physics 2007-05-23 Dorit Aharonov , Michael Ben-Or

Demonstrating small error rates by integrating quantum error correction (QEC) into an architecture of quantum computing is the next milestone towards scalable fault-tolerant quantum computing (FTQC). Encoding logical qubits with…

Quantum Physics · Physics 2025-01-03 Yasunari Suzuki , Takanori Sugiyama , Tomochika Arai , Wang Liao , Koji Inoue , Teruo Tanimoto

In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…

Quantum Physics · Physics 2015-08-18 Alexandru Paler , Simon J. Devitt

Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster…

Quantum Physics · Physics 2022-01-05 Blayney W. Walshe , Rafael N. Alexander , Nicolas C. Menicucci , Ben Q. Baragiola

This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum…

Quantum Physics · Physics 2009-11-11 Michael A. Nielsen

Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…

Quantum Physics · Physics 2025-08-15 Zhiyang He , Quynh T. Nguyen , Christopher A. Pattison

Symmetry-protected topological (SPT) phases are fundamental features of cluster states, serving as key resources for measurement-based quantum computation (MBQC). Generating large-scale cluster states and verifying their SPT phases are…

Quantum Physics · Physics 2026-04-06 Tao Jiang , Jianbin Cai , Junxiang Huang , Naibin Zhou , Yukun Zhang , Jiahao Bei , Guoqing Cai , Sirui Cao , Fusheng Chen , Jiang Chen , Kefu Chen , Xiawei Chen , Xiqing Chen , Zhe Chen , Zhiyuan Chen , Zihua Chen , Wenhao Chu , Hui Deng , Zhibin Deng , Pei Ding , Xun Ding , Zhuzhengqi Ding , Shuai Dong , Bo Fan , Daojin Fan , Yuanhao Fu , Dongxin Gao , Lei Ge , Jiacheng Gui , Cheng Guo , Shaojun Guo , Xiaoyang Guo , Lianchen Han , Tan He , Linyin Hong , Yisen Hu , He-Liang Huang , Yong-Heng Huo , Zuokai Jiang , Honghong Jin , Yunxiang Leng , Dayu Li , Dongdong Li , Fangyu Li , Jiaqi Li , Jinjin Li , Junyan Li , Junyun Li , Na Li , Shaowei Li , Wei Li , Yuhuai Li , Yuan Li , Futian Liang , Xuelian Liang , Nanxing Liao , Jin Lin , Weiping Lin , Dailin Liu , Hongxiu Liu , Maliang Liu , Xinyu Liu , Xuemeng Liu , Yancheng Liu , Haoxin Lou , Yuwei Ma , Lingxin Meng , Hao Mou , Kailiang Nan , Binghan Nie , Meijuan Nie , Jie Ning , Le Niu , Wenyi Peng , Haoran Qian , Hao Rong , Tao Rong , Huiyan Shen , Qiong Shen , Hong Su , Feifan Su , Chenyin Sun , Liangchao Sun , Tianzuo Sun , Yingxiu Sun , Yimeng Tan , Jun Tan , Longyue Tang , Wenbing Tu , Jiafei Wang , Biao Wang , Chang Wang , Chen Wang , Chu Wang , Jian Wang , Liangyuan Wang , Rui Wang , Shengtao Wang , Xiaomin Wang , Xinzhe Wang , Xunxun Wang , Yeru Wang , Zuolin Wei , Jiazhou Wei , Dachao Wu , Gang Wu , Jin Wu , Yulin Wu , Shiyong Xie , Lianjie Xin , Yu Xu , Chun Xue , Kai Yan , Weifeng Yang , Xinpeng Yang , Yang Yang , Yangsen Ye , Zhenping Ye , Chong Ying , Jiale Yu , Qinjing Yu , Wenhu Yu , Xiangdong Zeng , Chen Zha , Shaoyu Zhan , Feifei Zhang , Haibin Zhang , Kaili Zhang , Wen Zhang , Yiming Zhang , Yongzhuo Zhang , Lixiang Zhang , Guming Zhao , Peng Zhao , Xintao Zhao , Youwei Zhao , Zhong Zhao , Luyuan Zheng , Fei Zhou , Liang Zhou , Na Zhou , Shifeng Zhou , Shuang Zhou , Zhengxiao Zhou , Chengjun Zhu , Qingling Zhu , Guihong Zou , Haonan Zou , Qiang Zhang , Chao-Yang Lu , Cheng-Zhi Peng , Xiao Yuan , Ming Gong , Xiaobo Zhu , Jian-Wei Pan

Achieving fault-tolerant quantum computation (FTQC) demands simultaneous progress in physical qubit performance and quantum error correction (QEC). This work reviews and benchmarks experimental advancements towards FTQC across leading…

Quantum Physics · Physics 2025-07-08 François-Marie Le Régent

Blind quantum computation (BQC) enables a client with less quantum computational ability to delegate her quantum computation to a server with strong quantum computational power while preserving the client's privacy. Generally, many-qubit…

Quantum Physics · Physics 2022-01-11 Xiaoqian Zhang

Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and…

Distributed quantum computing (DQC) is a promising technique for scaling up quantum systems. While significant progress has been made in DQC for quantum circuit models, there exists much less research on DQC for measurement-based quantum…

Quantum Physics · Physics 2026-01-05 Yecheng Xue , Rui Yang , Zhiding Liang , Tongyang Li

Quantum computers promise ultrafast performance of certain tasks. Experimentally appealing, measurement-based quantum computation (MBQC) requires an entangled resource called a cluster state, with long computations requiring large cluster…

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