Halving the cost of surface codes by running error correction at the logical level
Talkat Near-Term Quantum Computers: Fault Tolerance + Benchmarking + Quantum Advantage + Quantum Algorithms · 2024-04-22..04-26·
summary
Proposes concatenating small rotated surface-code patches into a top-level parity code called yoked surface codes and measuring logical parities by lattice surgery, using the simple n,n-2,2 error-detecting code plus row/column checks. At physical error rate ~10^-3, analysis (circuit-level simulation + path-counting) yields ~1,000 qubits per logical for standard surface code, ~500–600 for 1D yoked layouts and ~350 for dense 2D yoked layouts to reach ~10^-12–10^-14 logical error rates. Simulations and decoding heuristics (complementary-gap soft information) show the scheme works with fault-tolerant measurement repetition and shared ancilla workspace.
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chapters (15)
- 0:00Introduction
- 1:20Why do we like surface codes
- 4:00The idea
- 5:20Quantum error correction
- 6:40Yolked surface codes
- 7:45LTIS surgery
- 9:23How does the scheme work
- 10:50Soft information
- 11:40Complimentary Gap
- 13:30Fault Tolerance
- 16:30Surface Codes
- 18:05Measuring Surface Codes
- 22:54Overhead Savings
- 25:48Future Directions
- 28:20Questions
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