subsystem quantum codes

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Recently, a new quantum LDPC code, the Subsystem Hypergraph Product Simplex (SHYPS) code, was introduced. It utilizes the Subsystem Hypergraph Product (SHGP) for code construction. ✨ This presents a fascinating use case of the SHGP framework (subsystem quantum codes) in building a quantum LDPC codes!

This nice paper provides the code construction for the two families of the quantum subsystem codes:

graph TD
    A[Subsystem quantum codes] -->|Family 1| B[Bravyi-Bacon-Shor codes]
    A -->|Family 2| C[Subsystem hypergraph product codes]

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Describe the solution you’d like

• Bravyi-Bacon-Shor code
• Subsystem Hypergraph Product (SHGP) code

Additional context

Kenneth and Isaac have done inspiring and exciting work on SubsystemCodeTableau and new group theory tools for QEC! It might also be probably related and helpful in the present context of subsystem quantum codes: grouptableaux.jl ✨ This topic appears to be closely related to the excellent work by Kenneth and Isaac on more general QECCs in #293!