On the Exploration of Quantum Polar Stabilizer Codes and Quantum Stabilizer Codes with High Coding Rate

• Published in: Entropy (Basel, Switzerland) Vol. 26; no. 10; p. 818
• Main Authors: Yi, Zhengzhong, Liang, Zhipeng, Wu, Yulin, Wang, Xuan
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 25-09-2024; MDPI
• Subjects: Algorithms; Atoms; classical polar codes; Codes; Coding; coding rate; Construction; Error correction & detection; error-correcting capability; logical error rate; Polarization; Quantum computing; Quantum dots; quantum error correction codes; Quantum phenomena; quantum polar stabilizer codes; Simulation; error-correcting capability; quantum polar stabilizer codes; quantum error correction codes; coding rate; logical error rate; classical polar codes
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e26100818

Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet. There are two intuitions in previous research. The first is that directly converting classical polar coding circuits to quantum ones will produce the polarization phenomenon of a pure quantum channel, which has been proved in our previous work. The second is that based on this quantum polarization phenomenon, one can design a quantum polar coding scheme that applies to quantum computing. There are several previous work following the second intuition, none of which has been verified by experiments. In this paper, we follow the second intuition and propose a more reasonable quantum polar stabilizer code construction algorithm than any previous ones by using the theory of stabilizer codes. Unfortunately, simulation experiments show that even the stabilizer codes obtained from this more reasonable construction algorithm do not work, which implies that the second intuition leads to a dead end. Based on the analysis of why the second intuition does not work, we provide a possible future direction for designing quantum stabilizer codes with a high coding rate by borrowing the idea of classical polar codes. Following this direction, we find a class of quantum stabilizer codes with a coding rate of 0.5, which can correct two of the Pauli errors.