Enhanced Fault-Tolerant Quantum Computing in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-Level Systems

Summary

This paper presents new error-correcting codes for d-level qudit systems with prime d, offering enhanced fault-tolerant quantum computing capabilities by enabling transversal non-Clifford gates and improving magic-state distillation performance with increasing d.

Key findings

• Codes for d-level qudit systems with prime d are presented.
• These codes possess transversal non-Clifford gates.
• The codes can detect up to ~d/3 errors.
• Performance in magic-state distillation is enhanced by increasing d.

Methods

• Development of error-correcting codes for d-level qudit systems.
• Analysis of the codes' ability to detect errors.
• Quantification of code performance in magic-state distillation.

Limitations

• The codes are presented for d-level qudit systems with prime d.
• The abstract does not detail specific experimental implementations or limitations thereof.

Applications

• Fault-tolerant quantum computing.
• Quantum error correction.
• Magic-state distillation.