Equal Opportunity Grant 2024
?berblick
Our project aims to advance the field of quantum error correction by exploring the construction of quantum error correcting codes and developing a general framework for their application in quantum computers and communications. By leveraging multipartite highly entangled states, which are fundamental to constructing holographic codes, we seek to compare and optimize quantum error correcting codes and tensor networks derived from these states. This research will enhance our understanding of quantum information processing and contribute to the development of robust quantum communication systems.
Motivation
Quantum error correction is crucial for the reliable operation of quantum computers and communication networks. Despite significant progress, there remains a need to broaden our knowledge on constructing optimal quantum error correcting codes and understanding their relationship with holographic codes. By investigating the classification of multipartite highly entangled states and their application in tensor networks, we aim to uncover new methods for error correction that can improve the performance and scalability of quantum systems.
Ziele und Vorgehen
The primary objective of this research is to develop a comprehensive understanding of quantum error correcting codes and their construction from highly entangled states. We will explore the classification of these states into locally unitary equivalent classes and compare the resulting quantum error correcting codes and tensor networks. Additionally, we aim to develop new encoding and decoding techniques based on the stabilizer formalism for transmitting both quantum and classical information. Our goal is to identify optimal quantum error correction codes with subspaces spanned by highly entangled tensor networks and to introduce innovative hybrid codes for enhanced quantum communication.
Innovation und Perspektiven
Our project introduces groundbreaking approaches to quantum error correction by integrating concepts from holographic codes and tensor networks. By establishing a connection between classical optimal codes, maximally multipartite entangled states, and quantum error correcting codes, we pave the way for the construction of optimal codes from highly entangled subspaces. Our research will also extend the connection between Absolutely Maximally Entangled (AME) states and quantum codes, providing larger code subspaces and introducing the Modified-Shortening construction. This innovative approach, which is explicit and physically motivated, will work with smaller local dimensions than previous codes with similar parameters, offering significant advancements in the field of quantum error correction.
Key Facts
- Laufzeit:
- 07/2024 - 07/2025
