Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0905.1542

Experimental demonstration of topological error correction

Weibo Gao, Austin G. Fowler, Robert Raussendorf, Xing-Can Yao, Lu, He, Xu, Ping, Lu, Chao-Yang, Peng, Cheng-Zhi, Youjin Deng, Chen, Zeng-Bing, Jian-Wei Pan

Published May 11, 2009• 1 citation
arXivHTMLPDF

Abstract

Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only nearest-neighbour interaction, particularly suitable for most physical systems. Here we report the first experimental demonstration of topological error correction with an 8-qubit optical cluster state. In the experiment, it is shown that a correlation can be protected against a single error on any single qubit. In addition, when all qubits are simultaneously subjected to errors with equal probability, the effective error rate is significantly reduced, clearly verifying the advantage of topological error correction. The quantum gate with the error rate below the threshold is within the current experimental technology. We believe topological error correction should be a critical ingredient for the future large-scale quantum computation.

DOI
10.48550/arxiv.0905.1542

Related papers

Topological error correction with a Gaussian cluster state

Shuhong Hao, Meihong Wang, Dong Wang +1 more

Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with a higher error threshold and high tolerating loss rates. We present a topological error correction scheme with continuous variables based on an eight-partite Gaussian cluster state. We show that topological quantum correlation between two modes can be protected against a single quadrature phase displacement error occurring on any mode and some of two errors occurring on two modes. More interestingly, some cases of errors occurring on three modes can also be recognized and corrected, which is different from the topological error correction with discrete variables. We show that the final error rate after correction can be further reduced if the modes are subjected to identical errors occurring on all modes with equal probability. The presented results provide a feasible scheme for topological error correction with continuous variables and it can be experimentally demonstrated with a Gaussian cluster state.

arXiv:2105.06012•Physical Review A•May 10, 2021•5 citations

High-threshold topological quantum error correction against biased noise

Ashley M. Stephens, William J. Munro, Kae Nemoto

Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can tolerate realistically high error rates will be necessary. In some physical systems, errors may exhibit a characteristic structure that can be carefully exploited to improve the efficacy of error correction. Here we describe a scheme for topological quantum error correction to protect quantum information from a dephasing-biased error model, where we combine a repetition code with a topological cluster state. We find that the scheme tolerates error rates of up to 1.37%--1.83% per gate, requiring only short-range interactions in a two-dimensional array.

arXiv:1308.4776•Physical Review A•Dec 10, 2013•35 citations

Topological Quantum Error Correction Realization via Topological Quantum Computers

Jincheng Zhang

This paper investigates the potential of utilizing topological quantum computers to achieve robust quantum error correction. The core claim centers on leveraging the unique physical properties of topological quantum computers – specifically, their inherent topological protection – to implement topological quantum error correction schemes. The proposed mechanism involves designing a quantum error-correcting code based on the interactions between entangled topological qubits within a physical topological structure. This approach allows for distributed error detection and correction, theoretically offering superior error correction rates and reduced resource requirements compared to traditional, single-qubit-based methods. The work explores the fundamental principles and theoretical framework for achieving topological quantum error correction, outlining key considerations for code design, qubit connectivity, and error mitigation strategies. The central focus is on demonstrating the feasibility of a topologically protected quantum code, contributing to the advancement of fault-tolerant quantum computing.

•Aug 31, 2026•0 citations

Modern Approaches to Topological Quantum Error Correction

Pedro Parrado-Rodríguez

The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of complex problems such as factoring large numbers, quick database search, and the quantum simulation of many-body quantum systems in fields as diverse as condensed matter, quantum chemistry, and even high-energy physics. Sophisticated theoretical protocols for reliable quantum information processing under imperfect conditions have been de-veloped, when errors affect and corrupt the fragile quantum states during storage and computations. Arguably, the most realistic and promising ap-proach towards practical fault-tolerant quantum computation are topologi-cal quantum error-correcting codes, where quantum information is stored in interacting, topologically ordered 2D or 3D many-body quantum systems. This approach offers the highest known error thresholds, which are already today within reach of the experimental accuracy in state-of-the-art setups. A combination of theoretical and experimental research is needed to store, protect and process fragile quantum information in logical qubits effectively so that they can outperform their constituting physical qubits. Whereas small-scale quantum error correction codes have been implemented, one of the main theoretical challenges remains to develop new and improve existing efficient strategies (so-called decoders) to derive (near-)optimal error cor-rection operations in the presence of experimentally accessible measurement information and realistic noise sources. One main focus of this project is the development and numerical implementation of scalable, efficient decoders to operate topological color codes. Additionally, we study the feasibility of im-plementing quantum error-correcting codes fault-tolerantly in near-term ion traps. To this end, we use realistic modeling of the different noise sources, computer simulations, and most modern quantum information approaches to quantum circuitry and noise suppression techniques.

•Jan 1, 2022•0 citations

Fault-tolerant topological cluster state quantum computing

Austin G. Fowler, Kovid Goyal

Introduction Cluster states were introduced in Chapter 18, along with some of the approaches to achieving fault tolerance in measurement-based quantum computing. In this chapter, we describe an extremely promising fault-tolerant cluster state quantum computing scheme [RH07, RHG07] with a threshold error rate of 7.46 × 10 −3 , low overhead arbitrarily long-range logical gates and novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only. Detailed proposed implementations of this scheme exist for ion traps [SJ09] and single photons with cavity mediated interactions [DGI+07]. The discussion is organized as follows. In Section 20.2, we describe the topological cluster state, which is a specific three-dimensional (3D) cluster state, and give a brief overview of what topological cluster state quantum computing involves. Section 20.3 describes logical qubits in more detail and how to initialize them to ∣0 L 〉 and ∣+ L 〉 and measure them in the Z L and X L bases. State injection, the non-fault-tolerant construction of arbitrary logical states, is covered in Section 20.4. Logical gates, namely the logical identity gate and the logical CNOT gate, are discussed in Section 20.5 along with their byproduct operators. Section 20.6 describes the errorcorrection procedure. In Section 20.7, we calculate an estimate for the threshold of this scheme. Section 20.8 presents an analysis of the overhead as a function of both the circuit size and the error rate.

Cambridge University Press eBooks•Sep 5, 2013•1 citation

Topological Cluster State Computation with Photons

Simon J. Devitt, Austin G. Fowler, Ashley M. Stephens +4 more

Entanglement is one of the most mysterious and fleeting properties of nature. It is also a powerful resource for quantum information processing. Efforts to design and build a quantum computer are severely constrained by the difficulties of preserving useful qubit entanglement against the environment. Concatenated fault-tolerant error correction provides a framework to perform scalable computation, but is extremely expensive in terms of resources. Direct topological implementations promise robust entanglement and control, but require physical systems with as yet unobserved controllable topological phases. Here we present the first practical scheme for constructing a topological quantum computer based on a 3D cluster state lattice of photons on chip. In contrast to the resource requirements of other schemes, a target error rate of 10^(-16) requires approximately 3000 components per logical qubit. This constitutes a significant advance towards practical quantum computing and leads the way for topological architectures in other implementations.

•Aug 13, 2008•9 citations
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only nearest-neighbour interaction, particularly suitable for most physical systems. Here we report the first experimental demonstration of topological error correction with an 8-qubit optical cluster state. In the experiment, it is shown that a correlation can be protected against a single error on any single qubit. In addition, when all qubits are simultaneously subjected to errors with equal probability, the effective error rate is significantly reduced, clearly verifying the advantage of topological error correction. The quantum gate with the error rate below the threshold is within the current experimental technology. We believe topological error correction should be a critical ingredient for the future large-scale quantum computation.
Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with a higher error threshold and high tolerating loss rates. We present a topological error correction scheme with continuous variables based on an eight-partite Gaussian cluster state. We show that topological quantum correlation between two modes can be protected against a single quadrature phase displacement error occurring on any mode and some of two errors occurring on two modes. More interestingly, some cases of errors occurring on three modes can also be recognized and corrected, which is different from the topological error correction with discrete variables. We show that the final error rate after correction can be further reduced if the modes are subjected to identical errors occurring on all modes with equal probability. The presented results provide a feasible scheme for topological error correction with continuous variables and it can be experimentally demonstrated with a Gaussian cluster state.
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can tolerate realistically high error rates will be necessary. In some physical systems, errors may exhibit a characteristic structure that can be carefully exploited to improve the efficacy of error correction. Here we describe a scheme for topological quantum error correction to protect quantum information from a dephasing-biased error model, where we combine a repetition code with a topological cluster state. We find that the scheme tolerates error rates of up to 1.37%--1.83% per gate, requiring only short-range interactions in a two-dimensional array.
This paper investigates the potential of utilizing topological quantum computers to achieve robust quantum error correction. The core claim centers on leveraging the unique physical properties of topological quantum computers – specifically, their inherent topological protection – to implement topological quantum error correction schemes. The proposed mechanism involves designing a quantum error-correcting code based on the interactions between entangled topological qubits within a physical topological structure. This approach allows for distributed error detection and correction, theoretically offering superior error correction rates and reduced resource requirements compared to traditional, single-qubit-based methods. The work explores the fundamental principles and theoretical framework for achieving topological quantum error correction, outlining key considerations for code design, qubit connectivity, and error mitigation strategies. The central focus is on demonstrating the feasibility of a topologically protected quantum code, contributing to the advancement of fault-tolerant quantum computing.
The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of complex problems such as factoring large numbers, quick database search, and the quantum simulation of many-body quantum systems in fields as diverse as condensed matter, quantum chemistry, and even high-energy physics. Sophisticated theoretical protocols for reliable quantum information processing under imperfect conditions have been de-veloped, when errors affect and corrupt the fragile quantum states during storage and computations. Arguably, the most realistic and promising ap-proach towards practical fault-tolerant quantum computation are topologi-cal quantum error-correcting codes, where quantum information is stored in interacting, topologically ordered 2D or 3D many-body quantum systems. This approach offers the highest known error thresholds, which are already today within reach of the experimental accuracy in state-of-the-art setups. A combination of theoretical and experimental research is needed to store, protect and process fragile quantum information in logical qubits effectively so that they can outperform their constituting physical qubits. Whereas small-scale quantum error correction codes have been implemented, one of the main theoretical challenges remains to develop new and improve existing efficient strategies (so-called decoders) to derive (near-)optimal error cor-rection operations in the presence of experimentally accessible measurement information and realistic noise sources. One main focus of this project is the development and numerical implementation of scalable, efficient decoders to operate topological color codes. Additionally, we study the feasibility of im-plementing quantum error-correcting codes fault-tolerantly in near-term ion traps. To this end, we use realistic modeling of the different noise sources, computer simulations, and most modern quantum information approaches to quantum circuitry and noise suppression techniques.
Introduction Cluster states were introduced in Chapter 18, along with some of the approaches to achieving fault tolerance in measurement-based quantum computing. In this chapter, we describe an extremely promising fault-tolerant cluster state quantum computing scheme [RH07, RHG07] with a threshold error rate of 7.46 × 10 −3 , low overhead arbitrarily long-range logical gates and novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only. Detailed proposed implementations of this scheme exist for ion traps [SJ09] and single photons with cavity mediated interactions [DGI+07]. The discussion is organized as follows. In Section 20.2, we describe the topological cluster state, which is a specific three-dimensional (3D) cluster state, and give a brief overview of what topological cluster state quantum computing involves. Section 20.3 describes logical qubits in more detail and how to initialize them to ∣0 L 〉 and ∣+ L 〉 and measure them in the Z L and X L bases. State injection, the non-fault-tolerant construction of arbitrary logical states, is covered in Section 20.4. Logical gates, namely the logical identity gate and the logical CNOT gate, are discussed in Section 20.5 along with their byproduct operators. Section 20.6 describes the errorcorrection procedure. In Section 20.7, we calculate an estimate for the threshold of this scheme. Section 20.8 presents an analysis of the overhead as a function of both the circuit size and the error rate.
Entanglement is one of the most mysterious and fleeting properties of nature. It is also a powerful resource for quantum information processing. Efforts to design and build a quantum computer are severely constrained by the difficulties of preserving useful qubit entanglement against the environment. Concatenated fault-tolerant error correction provides a framework to perform scalable computation, but is extremely expensive in terms of resources. Direct topological implementations promise robust entanglement and control, but require physical systems with as yet unobserved controllable topological phases. Here we present the first practical scheme for constructing a topological quantum computer based on a 3D cluster state lattice of photons on chip. In contrast to the resource requirements of other schemes, a target error rate of 10^(-16) requires approximately 3000 components per logical qubit. This constitutes a significant advance towards practical quantum computing and leads the way for topological architectures in other implementations.