Quantum Pin Codes

Abstract

We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an unfolding procedure and their stabilizers form so-called $\ell$-orthogonal spaces meaning that the joint overlap between any $\ell$ stabilizer elements is always even. This last feature makes them interesting for devising magic-state distillation protocols, for instance by using puncturing techniques. We study examples of these codes and their properties.

21 pages, 10 figures

References in corpus (9)

• Topological Quantum Distillation
• Magic state distillation with low overhead
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• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Universal transversal gates with color codes - a simplified approach
• Multilevel distillation of magic states for quantum computing
• Diagonal gates in the Clifford hierarchy
• On Optimality of CSS Codes for Transversal $T$

Cited by in corpus (9)

• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Designing the Quantum Channels Induced by Diagonal Gates
• Quantum XYZ Product Codes
• Mitigating Coherent Noise by Balancing Weight-2 $Z$-Stabilizers
• Fault-tolerant logical measurements via homological measurement
• Geometric structure and transversal logic of quantum Reed-Muller codes
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
• Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates)
• Coxeter codes: Extending the Reed-Muller family