Mathematical Analysis and Explicit Construction of a Rectangular CSS Surface Code with Parameters [1024, 16, 8]

Key Points

• To construct and analyze a CSS surface code on a 64x16 qubit lattice encoding 16 logical qubits in 1024 physical qubits at distance 8.
• Conducted mathematical analysis and construction of a CSS surface code.
• Provided explicit algebraic definitions, geometric proofs, and GF(2) rank calculations.
• Developed executable Python code to support findings.
• Successfully encoded k=16 logical qubits within n=1024 physical qubits at a code distance of d=8.
• Demonstrated robustness through exhaustive mathematical proofs and calculations.
• Validated approach with implemented Python code, facilitating practical use.