Quantum Error Correction
In classical computing, coding theory is an essential field of research with widespread influence in both theory and practical applications, e.g., Wifi, Bluetooth, and 4G/5G. The nature of qubits and quantum operations in quantum computing is very fragile and error-prone, which leads to the fact that quantum algorithms are currently unusable in practice and quantum advantage is out of reach. Thus, Quantum Error-Correction (QEC), i.e., methods to protect quantum information from noise, is a crucial field of research towards the realization of quantum computers. Currently, it is still unclear what the best QEC protocol is, or which protocol should be used for what scenarios. There are several factors that influence the optimal choice of Quantum Error-Correcting Code (QECC) to implement, e.g., architectural constraints of physical devices, ability of logical operations, and scalability. It is therefore crucial to develop both theoretical groundwork and QEC methods that are physically more realistic and realizable.
On this page, we summarize our work on QEC which includes both, theoretical work on state-of-the-art quantum codes and decoding algorithms, and the implementation of open-source software tools for QEC and thereby lies on the interface between theoretical groundwork and practical applications.
All proposed software tools have been implemented in the open-source quantum error-correction tool QECC as part of the open-source Munich Quantum Toolkit (MQT).
In case of questions/problems, don’t hesitate to contact us via quantum.cda@xcit.tum.de, or by creating an issue on GitHub.
Low-Density Parity-Check Quantum Codes
Motivated by a series of recent breakthrough results around asymptotically good quantum codes, low-density parity-check quantum codes (QLDPC codes) have been proposed as a promising candidate for QEC. Compared to the well-established Surface Codes, there are many open questions regarding QLDPC codes, e.g., decoding, practicality w.r.t. physical realization on quantum architectures, and logical operations. We develop both, theoretical groundwork on QLDPC codes, and software tools for QLDPC codes to provide publicly available software tools for the community.
Decoding Low-Density Parity-Check Quantum Codes
Decoding is a central problem in QEC, however, the availability of state-of-the-art open-source decoders is limited. We propose an implementation of the Union-Find decoding algorithm for quantum LDPC codes and propose a heuristic that eliminates runtime bottlenecks of the original decoder.
Details are discussed in the corresponding paper “Software Tools for Decoding Quantum Low-Density Parity-Check Codes” [pdf].
@inproceedings{berent2023software,
title = {Software Tools for Decoding Quantum Low-Density Parity-Check Codes},
author = {Berent, Lucas and Burgholzer, Lukas and Wille, Robert},
booktitle = {Proceedings of the 28th Asia and South Pacific Design Automation Conference},
pages = {709--714},
year = {2023}
}
QLDPC Codes For Modular Architectures
It is unclear how QLDPC codes can be implemented from a physical perspective. Since they require long-range connectivity, this is a highly non-trivial problem. Currently, modular quantum architectures are a promising candidate to scale up quantum systems. In this work, we propose a rigorous method to take a first step towards closing the gap between code constructions and physical system architectures. We show that there is a connection between modular layouts and quantum code constructions and thereby propose a recipe for how codes for modular architectures can be constructed (for a summary see also popular summary).
Details are discussed in the corresponding paper “Quantum LDPC Codes for Modular Architectures” [pdf].
@article{strikis2022quantum,
title = {Quantum LDPC Codes for Modular Architectures},
author = {Strikis, Armands and Berent, Lucas},
journal = {arXiv preprint arXiv:2209.14329},
year = {2022}
}
Topological Quantum Codes
Topological Quantum codes are a class of quantum error-correcting codes that ensure locality of operations which is advantageous for practical implementations.
Decoding Quantum Color Codes
Quantum Color Codes are a promising class of Topological Quantum codes due to favorable properties such as locality and the ability to perform logical operations. We propose a MaxSAT decoder for Color Codes based on an analogy with the well-known LightsOut puzzle. The decoding performance is near optimal (for bit-flip noise) and numerical experiments show that it outperforms existing implementations (in the sub-threshold region).
Details are discussed in the corresponding paper “Decoding Quantum Color Codes with MaxSAT” [pdf].
@article{berent2023decoding,
title = {Decoding Quantum Color Codes with MaxSAT},
author = {Berent, Lucas and Burgholzer, Lucas and Ders, Peter-Jan H.S. and Eisert, Jens and Wille, Robert},
journal = {arXiv preprint arXiv:2303.14237},
year = {2023}
}
Applying Quantum Codes to Circuits
The goal of Fault-Tolerance is to protect quantum circuits from noise. Thus, the qubits as well as every operation has to be protected using an error-correcting code. In this work, we propose a method to apply quantum codes to quantum circuits in an automated fashion. Furthermore, the resulting circuit can then be simulated in a noise-aware fashion.
Details are discussed in the corresponding paper “Automatic Implementation and Evaluation of Error-Correcting Codes for Quantum Computing: An Open-Source Framework for Quantum Error Correction” [pdf].
@article{grurl2023automatic,
title = {Automatic Implementation and Evaluation of Error-Correcting Codes for Quantum Computing: An Open-Source Framework for Quantum Error Correction},
author = {Grurl, Thomas and Pichler, Christoph and Fu{\ss}, J{\"u}rgen and Wille, Robert},
journal = {arXiv preprint arXiv:2301.05731},
year = {2023}
}