Universal Framework for Quantum Error-Correcting Codes
Zhuo Li, Li-Juan Xing
TL;DR
This paper introduces a universal algebraic framework for quantum error-correcting codes based on group algebra, enabling comprehensive characterization and new insights into quantum code properties.
Contribution
It develops a general group algebra-based framework that applies to all quantum error-correcting codes, facilitating analysis and discovery of new code properties.
Findings
Framework characterizes quantum code properties via group algebra
Generates new results about quantum codes
Unifies analysis of diverse quantum error-correcting codes
Abstract
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum-Dot Cellular Automata