{ "seed": 1620, "predictions": [ "For every N=2^k, ||T x||/||x|| = 1 exactly up to floating point.", "T^*T-I is at machine precision and does not grow materially with N.", "If every local gate is scaled by 1+eps, repeated-pass norm drift is (1+eps)^(k*r), k=log2(N)." ], "unitarity_sweep": [ { "N": 4, "levels": 2, "unitarity_fro_error": 6.518129683673256e-16, "norm_ratio": 1.0, "predicted_norm_ratio": 1.0 }, { "N": 8, "levels": 3, "unitarity_fro_error": 1.4324005761866033e-15, "norm_ratio": 1.0, "predicted_norm_ratio": 1.0 }, { "N": 16, "levels": 4, "unitarity_fro_error": 3.1637566171101538e-15, "norm_ratio": 0.9999999999999998, "predicted_norm_ratio": 1.0 }, { "N": 32, "levels": 5, "unitarity_fro_error": 3.95486773296341e-15, "norm_ratio": 0.9999999999999998, "predicted_norm_ratio": 1.0 }, { "N": 64, "levels": 6, "unitarity_fro_error": 7.607348859942032e-15, "norm_ratio": 0.9999999999999999, "predicted_norm_ratio": 1.0 } ], "controlled_drift": [ { "epsilon": 0.0, "repetitions": 1, "observed": 0.9999999999999998, "predicted": 1.0, "relative_error": 2.220446049250313e-16 }, { "epsilon": 0.0, "repetitions": 4, "observed": 0.9999999999999989, "predicted": 1.0, "relative_error": 1.1102230246251565e-15 }, { "epsilon": 0.0, "repetitions": 8, "observed": 0.9999999999999986, "predicted": 1.0, "relative_error": 1.4432899320127035e-15 }, { "epsilon": 0.001, "repetitions": 1, "observed": 1.0050100100050003, "predicted": 1.0050100100050003, "relative_error": 0.0 }, { "epsilon": 0.001, "repetitions": 4, "observed": 1.0201911448605396, "predicted": 1.0201911448605405, "relative_error": 8.706000088067209e-16 }, { "epsilon": 0.001, "repetitions": 8, "observed": 1.0407899720518592, "predicted": 1.0407899720518605, "relative_error": 1.2800542523711052e-15 }, { "epsilon": 0.01, "repetitions": 1, "observed": 1.0510100500999997, "predicted": 1.0510100501000001, "relative_error": 4.2253564540872753e-16 }, { "epsilon": 0.01, "repetitions": 4, "observed": 1.2201900399479657, "predicted": 1.220190039947967, "relative_error": 1.0918525688072328e-15 }, { "epsilon": 0.01, "repetitions": 8, "observed": 1.4888637335882187, "predicted": 1.4888637335882213, "relative_error": 1.7896434703790782e-15 }, { "epsilon": 0.05, "repetitions": 1, "observed": 1.2762815625, "predicted": 1.2762815625000004, "relative_error": 3.479555161638265e-16 }, { "epsilon": 0.05, "repetitions": 4, "observed": 2.6532977051444195, "predicted": 2.653297705144422, "relative_error": 1.0042353158992168e-15 }, { "epsilon": 0.05, "repetitions": 8, "observed": 7.039988712124649, "predicted": 7.039988712124658, "relative_error": 1.2616190963068666e-15 } ], "inverse_reconstruction_error": 3.935883022631844e-15, "toy_fit": { "N": 16, "samples": 256, "steps": 300, "structured_params": 128, "dense_complex_params": 256, "structured_final_mse": 2.6289821430935945e-09, "dense_final_mse": 6.717594010349423e-14, "structured_curve": [ 1.7592724561691284, 0.0034636000636965036, 1.7555914382683113e-05, 4.507657536123588e-08, 2.6289821430935945e-09 ], "dense_curve": [ 2.1629297733306885, 0.004571008030325174, 3.12544361804612e-05, 7.688760739199552e-10, 6.717594010349423e-14 ], "seconds": 15.026386260986328, "device": "cuda" } }