Quantum Lego: Quantum Codes and their Enumerators from Tensor Networks
Talkat Near-Term Quantum Computers: Fault Tolerance + Benchmarking + Quantum Advantage + Quantum Algorithms · 2024-04-22..04-26·
summary
Constructs large stabilizer codes by tracing small code tensors (not just restating the topic) and shows the core claim that the code’s quantum weight enumerators can be built from the Legos’ enumerators via tensor-network contraction so one can read exact distances and undetectable-error counts. Examples include 181-qubit surface code, distance 10, toric and Steane realizations from 4,2,2 Legos, and the practical result that exact integer enumerators computed in ~20 minutes on a laptop. The method proves a MacWilliams-style transform and that tensor enumerators trace to code enumerators.
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chapters (16)
- 0:00Quantum Lego intro
- 1:21Quantum codes from tensors
- 3:08Quantum codes as isometries
- 5:16Bacon-Shor code
- 7:45Operator pushing
- 9:11Surface code via tensors
- 11:20Surface code variants
- 14:12Color and Steane codes
- 16:40Quantum weight distributions
- 21:03MacWilliams identities
- 22:50Tensor enumerators
- 24:40Traced tensor enumerators
- 25:44Surface code enumerators
- 26:49Color code open questions
- 27:30Future directions
- 28:10Q&A
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