Add example: logical error rates under coherent rotation (CSS(RM(1,4),RM(1,4))) - #568
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sdoygb wants to merge 3 commits into
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Add example: logical error rates under coherent rotation (CSS(RM(1,4),RM(1,4)))#568sdoygb wants to merge 3 commits into
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Self-orthogonal CSS code family CSS(RM(r,m), RM(r,m)) with parameters
[[2^m, 2^m - 2*sum_{j<=r} C(m,j), 2^(r+1)]] for 2r < m-1.
- Stabilizer generators: rows of the RM(r,m) generator matrix
(pairwise orthogonal since RM(r,m) is strictly self-orthogonal)
- Closed-form distance 2^(r+1) via Reed-Muller minimum-weight theorem,
making distance evaluation O(1) instead of exponential in block length
- X/Z distances equal; promise_equal_distance_xz=True
- Closes qLDPCOrg#566
…nt rotation Exact (machine-precision) state-vector experiments on [[16,6,4]]: - Exp A: single-qubit detection rate = sin^2(theta/2), all Pauli types - Exp A1: weight-1 post-recovery loss < 1e-16 (directional completeness) - Exp B: logical Xbar flip = sin^2(theta/2), Zbar flip = 0 - Exp C: all-qubit random rotations, loss ~ 0.138 theta^4.05 (slope 4 = d) - Exp C2: uniform-angle R_X, slope 3.975, c -> 3.0 (closed form) - Exp D: weight-2 degeneracy: fail(2)=0.875, kappa=0.457, c_pred=3.0000 - Exp E: random-Pauli control: loss ~ p^1.8 (incoherent, slope -> 2) Theory: 10.29 / 10.31 / 10.35 / 10.36 (geometric theory framework).
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I am about to go on vacation, so I apologize advance that this may take me a few weeks to get to 🙂 |
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Closes #434 (part 2).
Exact state-vector verification of coherent-rotation logical error rates on
CSS(RM(1,4), RM(1,4)) = [[16,6,4]] (directionally complete, d = 4); companion
to the ReedMullerCSSCode class from #567.
All numbers are machine-precision exact: symbolic |0_L>, exact rotations,
stabilizer projections, min-weight lookup-table decoding, coherent loss
formula — no Monte Carlo, no Pauli twirling. Full run ≈ 66 s.