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

Area of Science:

• Quantum Information Science
• Quantum Computing
• Error Correction Codes

Background:

• Classical polar codes achieve Shannon capacity, motivating research into quantum analogs (quantum polar codes).
• Previous attempts to adapt classical polar coding to quantum computing have faced challenges.
• The quantum polarization phenomenon in pure quantum channels was previously established.

Purpose of the Study:

• To investigate the viability of constructing quantum polar coding schemes for quantum computing.
• To develop a novel quantum polar stabilizer code construction algorithm.
• To identify effective strategies for high-rate quantum error correction.

Main Methods:

• Utilized stabilizer code theory to construct quantum polar codes.
• Performed simulation experiments to evaluate the performance of the constructed codes.
• Analyzed the limitations of existing quantum polar coding intuitions.

Main Results:

• A proposed quantum polar stabilizer code construction algorithm, though improved, did not yield functional codes for quantum computing.
• Simulation results indicated that the second intuition for quantum polar coding is a dead end.
• A new class of quantum stabilizer codes with a 0.5 coding rate was discovered.

Conclusions:

• The direct application of quantum polarization phenomenon for quantum computing via stabilizer codes is not fruitful.
• Future research should explore alternative strategies inspired by classical polar codes for quantum stabilizer code design.
• The newly found quantum stabilizer codes demonstrate potential for correcting specific Pauli errors at a 0.5 coding rate.