FET: CIF: Small: Graph-Based Quantum Error Correcting Codes

FET：CIF：小型：基于图形的量子纠错码

• 批准号: 2007689
• 负责人: Javier Garcia-Frias
• 金额: $ 50万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2007689&HistoricalAwards=false
• 关键词: FET; CIF; Small; Graph; Based

Quantum computing is inherently noisy, and errors in the processed qubits are always present. In order to correct the errors, it is therefore necessary to apply quantum error-correcting codes, which will be a key component of future practical fault-tolerant quantum computation systems. Although existing practical quantum codes use very short block lengths, future practical systems will deal with many qubits and will need to apply powerful codes with long block lengths. This project investigates the construction of novel families of quantum codes that for long block lengths are expected to achieve excellent performance in practical scenarios. Two graduate students and two undergraduate students will directly participate in this research, and state of the art results from the project will be disseminated in a new graduate course developed by the PI.Specifically, this project investigates the application of turbo-like/graph-based coding structures in quantum error correction. The introduction of graph-based codes, which are iteratively decoded using message passing, has been one of the most important developments in classical communications during the last two decades, leading to excellent performance in many different environments when the block length increases. Interestingly, the quantum codes in the important family of stabilizer codes can be designed taking as a starting point classical graph-based codes that satisfy the symplectic property, which can be seen as a constraint in the graph structure. Following this approach, excellent results can be obtained for the subset of Calderbank-Short-Steane (CSS) quantum codes. By properly modifying the graph structure, this project will explore the great potential for the development of even better non-CSS stabilizer codes that can be applied in realistic quantum channels, such as asymmetric channels and channels with memory. The objective is to achieve improved performance even when the channel parameters are not known at the decoder site, by estimating them jointly with the decoding process, leading to more robust designs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

量子计算本身就有噪声，并且处理的量子比特中总是存在错误。为了纠正错误，因此有必要应用量子纠错码，这将是未来实用容错量子计算系统的关键组成部分。虽然现有的实用量子码使用非常短的块长度，但未来的实用系统将处理许多量子位，并且需要应用具有长块长度的强大代码。该项目研究了新型量子码族的构建，对于长块长度，这些量子码有望在实际场景中实现出色的性能。两名研究生和两名本科生将直接参与这项研究，该项目的最新成果将在PI开发的新研究生课程中传播。具体来说，该项目研究了类涡轮/基于图的编码结构在量子纠错中的应用。引入基于图的代码，使用消息传递迭代解码，是过去二十年来经典通信中最重要的发展之一，当块长度增加时，在许多不同的环境中具有出色的性能。有趣的是，稳定子码的重要家族中的量子码可以以满足辛性质的经典基于图的码为起点来设计，辛性质可以被视为图结构中的约束。按照这种方法，可以得到很好的结果的子集的Calderbank-Short-Steane（CSS）量子码。通过适当地修改图形结构，该项目将探索开发更好的非CSS稳定器代码的巨大潜力，这些代码可以应用于现实的量子信道，例如非对称信道和有记忆的信道。其目标是通过与解码过程共同估计信道参数，从而实现更高的性能，即使在解码器站点信道参数未知的情况下也是如此，从而实现更稳健的设计。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

On the Logical Error Rate of Sparse Quantum Codes

• DOI: 10.1109/tqe.2022.3196609
• 发表时间: 2021-08
• 期刊: IEEE Transactions on Quantum Engineering
• 作者: Patricio Fuentes;Josu Etxezarreta Martinez;P. Crespo;J. Garcia-Frías

Time-varying quantum channel models for superconducting qubits

• DOI: 10.1038/s41534-021-00448-5
• 发表时间: 2021-07
• 期刊: npj Quantum Information
• 影响因子: 7.6
• 作者: Josu Etxezarreta Martinez;Patricio Fuentes;P. Crespo;J. Garcia-Frías

Quantum outage probability for time-varying quantum channels

时变量子通道的量子中断概率

• DOI: 10.1103/physreva.105.012432
• 发表时间: 2022
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Etxezarreta Martinez, Josu;Fuentes, Patricio;Crespo, Pedro M.;Garcia-Frias, Javier
• 通讯作者: Garcia-Frias, Javier

Performance of non-CSS LDGM-based quantum codes over the misidentified depolarizing channel

基于非 CSS LDGM 的量子码在错误识别的去极化信道上的性能

• DOI: 10.1109/qce49297.2020.00022
• 发表时间: 2020
• 期刊: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE
• 作者: Fuentes, Patricio;Martinez, Josu Etxezarreta;Crespo, Pedro M.;Garcia-Frias, Javier
• 通讯作者: Garcia-Frias, Javier

Pauli Channel Online Estimation Protocol for Quantum Turbo Codes

量子 Turbo 码的泡利通道在线估计协议

• DOI: 10.1109/qce49297.2020.00023
• 发表时间: 2020
• 期刊: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE
• 作者: Martinez, Josu Etxezarreta;Fuentes, Patricio;Crespo, Pedro M.;Garcia-Frias, Javier
• 通讯作者: Garcia-Frias, Javier