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Paper · 2608.24229 · 2026

A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learning

Ziyu Zhang, Zikang Jia, Xiaosong Li, Yulong Dong

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 23 functions out of this paper's own repositories and ran 17 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
dongsnaq/Finite-Noise-Generalization-QML canonical 17 of 23
FunctionStatusWhere it lives
config_tasks Ran dongsnaq/Finite-Noise-Generalization-QML/code/run_checkpoint_sweep.py
code served (permissive licence) · get_code("17880e440501c4df")
custom_collate_fn Ran dongsnaq/Finite-Noise-Generalization-QML/code/qnir_molecular/model.py
code served (permissive licence) · get_code("2ce2388871b24883")
file_sha256 Ran dongsnaq/Finite-Noise-Generalization-QML/code/compute_molecular_deff.py
code served (permissive licence) · get_code("970994898fa7a46d")
fit_geff Ran dongsnaq/Finite-Noise-Generalization-QML/code/assemble_recomputed_results.py
code served (permissive licence) · get_code("662f42aff1ab732f")
jacobian_rows Ran dongsnaq/Finite-Noise-Generalization-QML/code/compute_molecular_deff.py
code served (permissive licence) · get_code("ca145de1d739f72a")
kron_all Ran dongsnaq/Finite-Noise-Generalization-QML/code/qnir_four_qubit/noise_order_dp.py
code served (permissive licence) · get_code("6f5062331e95e2c7")
load_gaussian_results Ran dongsnaq/Finite-Noise-Generalization-QML/code/qnir_four_qubit/noise_programming.py
code served (permissive licence) · get_code("f060c09b14d1af37")
load_molecular_metrics Ran dongsnaq/Finite-Noise-Generalization-QML/code/assemble_recomputed_results.py
code served (permissive licence) · get_code("66bcdfafd9203c52")
load_result_bundle Ran dongsnaq/Finite-Noise-Generalization-QML/code/result_bundle.py
code served (permissive licence) · get_code("845db32893fa3ca7")
molecular_task Ran dongsnaq/Finite-Noise-Generalization-QML/code/run_checkpoint_sweep.py
code served (permissive licence) · get_code("394bb51670197362")
mse Ran dongsnaq/Finite-Noise-Generalization-QML/code/evaluate_four_qubit_checkpoint.py
code served (permissive licence) · get_code("e06f503cace0223b")
noise_colors Ran dongsnaq/Finite-Noise-Generalization-QML/code/plot_style.py
code served (permissive licence) · get_code("0f18c20dcc62ba1e")
quantize_angle_ste Ran dongsnaq/Finite-Noise-Generalization-QML/code/qnir_molecular/model.py
code served (permissive licence) · get_code("6ac3321e493591f2")
rx Ran dongsnaq/Finite-Noise-Generalization-QML/code/qnir_four_qubit/noise_order_dp.py
code served (permissive licence) · get_code("b3f824c4f1955dcd")
sha256 Ran dongsnaq/Finite-Noise-Generalization-QML/code/evaluate_molecular_checkpoint.py
code served (permissive licence) · get_code("6f2a533d0951e650")
soft_count Ran dongsnaq/Finite-Noise-Generalization-QML/code/compute_molecular_deff.py
code served (permissive licence) · get_code("e1390a36e53bff7e")
summarize Ran dongsnaq/Finite-Noise-Generalization-QML/code/plot_figures.py
code served (permissive licence) · get_code("bf0c07b92ddcb985")
beta_x Not yet run dongsnaq/Finite-Noise-Generalization-QML/code/plot_figures.py
code served (permissive licence) · get_code("bc5582461119e4b0")
build_heatmap_arrays Not yet run dongsnaq/Finite-Noise-Generalization-QML/code/qnir_four_qubit/noise_programming.py
code served (permissive licence) · get_code("e2807313509bed37")
one_wire Not yet run dongsnaq/Finite-Noise-Generalization-QML/code/qnir_four_qubit/noise_order_dp.py
code served (permissive licence) · get_code("a03de0f3995024bc")
read_table Not yet run dongsnaq/Finite-Noise-Generalization-QML/code/plot_figures.py
code served (permissive licence) · get_code("4654b8eea9b271c2")
sector_purity Not yet run dongsnaq/Finite-Noise-Generalization-QML/code/assemble_recomputed_results.py
code served (permissive licence) · get_code("5e58fc0a4af6f6f6")
tasks Not yet run dongsnaq/Finite-Noise-Generalization-QML/code/run_checkpoint_sweep.py
code served (permissive licence) · get_code("6ef98b44594cd464")

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

Quantum noise is expected to degrade quantum machine learning by driving circuits away from their noiseless implementations. Yet recent studies show moderate noise can reduce testing error, a behavior unexplained by weak-noise perturbative error accumulation or strong-noise trainability collapse. Here we develop a statistical learning theory connecting microscopic noise processes to macroscopic learning performance. At its heart is a noise-order purity parameter, derived from a surrogate model analysis, that predicts the noise-induced reduction in model complexity and the consequent reduction in the generalization gap. Noise simultaneously increases prediction bias. Their competition explains the intermediate-noise regime left open between these limits. It produces a finite-noise optimum whose location depends on the learning setup and can disappear in the largesample limit. Numerical experiments validate these predictions. Noise programming can move a model towards this optimum. These results make the non-monotonic effect of noise predictable and provide a route to harness it.

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