A topological route to error correction

Jincheng Zhang

This paper investigates the application of topological coding to enhance quantum error correction. The core claim is that leveraging topological protection effects can optimize the error correction capability and transmission efficiency of quantum codes, while simultaneously reducing the sensitivity of quantum information to noise. We propose a novel quantum error correction code based on a topological network, exploiting the inherent robustness of topological states to mitigate the detrimental effects of noise. The underlying mechanism involves utilizing the topological protection effect to eliminate the influence of noise. The resulting code demonstrates improved error correction performance compared to conventional codes. This work contributes to the advancement of reliable quantum information transmission and processing by harnessing the unique properties of topological materials. The proposed framework offers a promising route toward building fault-tolerant quantum computers. Further research will focus on scaling up the topological code and exploring its integration with existing quantum technologies.

Xing-Can Yao, Tianxiong Wang, Hao-Ze Chen +9 more

Wei-Hsiang Tseng, Chen-Hao Hsu, Wan-Hsuan Lin +1 more

Topological quantum error correction (TQEC) is promising for scalable fault-tolerant quantum computation. The required resource of a TQEC circuit can be modeled as its space-time volume of a three-dimensional geometric description. Implementing a quantum algorithm with a reasonable physical qubit number and computation time is challenging for large-scale complex problems. Therefore, it is desirable to minimize the space-time volume for large-scale TQEC circuits. Previous work proposed bridge compression, which can significantly compress a TQEC circuit, but it was performed manually. This article presents the first automated tool that can perform bridge compression on a large-scale TQEC circuit. Our proposed algorithm applies the bridge compression technique to compactify TQEC circuits with modularization. Besides, we offer a time-ordering-aware 2.5-D placement for compacting TQEC circuits and satisfying time-ordered measurement constraints. On the other hand, we suggest friend net-aware routing to effectively reduce the required routing resource under topological deformation. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 84%.

Chiara Macchiavello, Guillermo Palma

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum technologies, presents significant challenges in terms of error correction and secure communication. Traditional error correction codes often rely on complex mathematical operations, introducing vulnerabilities. This paper introduces a novel quantum entanglement computation framework leveraging topological information, aiming to enhance the robustness and security of entanglement. We propose a quantum entanglement computation algorithm that utilizes the inherent topological properties of entangled states to achieve improved error correction and secure information transfer. This framework utilizes a dynamically constructed quantum state, exploiting topological features to effectively mitigate errors and safeguard sensitive information. The core mechanism revolves around designing a quantum state computation scheme intrinsically linked to topological structures. This approach offers a potential paradigm shift in the field, providing a more reliable and secure route to quantum technologies.

Sueli I. R. Costa, CÉsar Augusto Watanabe Dainezi