SIRIUS-14k: Barren Plateau Gradient Trajectory Dataset

13,800 labeled optimization trajectories across 4 VQA circuit architectures.

The first publicly released labeled dataset for barren plateau research in variational quantum algorithms. Contains gradient variance profiles, convergence diagnostics, and multi-label trainability annotations correcting the label ambiguity in prior work.

Central Finding

Analysis of this dataset reveals two architecturally distinct VQA training failure modes that prior work conflated under the single label "barren plateau":

Failure Mode	Architectures	Scaling exp. (α)	grad_var_ratio	Profile
Gradient-barren	StronglyEntangling, BasicEntangler	1.02, 1.01	0.38–0.62	Full DLA, exponential gradient decay
Restricted-DLA	RealAmplitudes, EfficientSU2	0.196, 0.169	96–165 (max 1631)	Constrained Hilbert subspace, gradient-rich

Gradient-barren circuits exhibit exponentially vanishing gradients (α ≈ 1.0). Restricted-DLA circuits have gradient variance substantially above the reference scale — optimisation does not stall due to vanishing gradients, but converges slowly due to the constrained subspace. The grad_var_ratio column normalises mean σ²_0 by the reference scale 2^{-n} (not the Haar-random Var_θ).

Dataset Statistics

Property	Value
Total trajectories	13,800
Configurations (n, d, arch)	276
Architectures	4
Qubits (n)	4, 6, 8, 10, 12, 14, 16
Circuit depths (d)	1 – 10
Seeds per configuration	50
Optimizer	SGD, η=0.1, 100 steps
Cost function	Local observable ⟨Z_0⟩
Simulator	PennyLane default.qubit (noiseless)
Per-trajectory labels	18
Per-configuration labels	24

Files

sirius_14k_trajectories_labeled.parquet   # 13,800 rows × 18 labels
sirius_14k_config_labeled.parquet         # 276 rows × 24 aggregate labels
trajectories_labeled_{arch}.parquet       # per-architecture splits (4 files)
config_labeled_{arch}.parquet             # per-architecture config splits (4 files)

Label Schema

Per-Trajectory Labels (18 fields)

Label	Type	Description
outcome	categorical	converged / barren_plateau / slow_convergent / stagnant
plateau_severity	categorical	none / mild / moderate / severe
loss_improvement	float	L(0) − L(T), total loss reduction
convergence_step	int	first step with cumulative improvement ≥ 95% of ΔL
plateau_onset_step	int	first step with σ²_t < 10⁻⁴
grad_var_t0	float	σ²_0 = Var_k[∂L/∂θ_k] at step 0
grad_var_early	float	mean σ²_t over steps 0–9
grad_var_final	float	mean σ²_t over steps 90–99
grad_var_decay_rate	float	log(σ²_final / σ²_0) / T
effective_dim	float	mean σ²_t / σ²_0 — gradient signal persistence
landscape_roughness	float	CV of per-step loss increments
trainability_lifetime	int	first t s.t. σ²_t < σ²_0 / e
curvature_proxy	float	mean |Δ‖∇L‖| per step

Note on outcome definition: The binary hits_plateau label conflates gradient decay at convergence (optimum found) with genuine barren plateau (gradient vanishes before progress). Our corrected two-signal schema fixes this: barren_plateau requires both σ²_t < 10⁻⁴ AND ΔL ≤ 0.2 (10% of dynamic range).

Per-Configuration Labels (24 fields, aggregated over 50 seeds)

Label	Description
converged_rate	Fraction of seeds reaching convergence (ΔL > 1.0)
barren_rate	Fraction of seeds hitting genuine barren plateau
slow_rate	Fraction in slow-convergent regime
mean/std/median_grad_var_t0	Initial gradient variance statistics
grad_var_scaling_exp	Fitted α from σ²_0 ∝ 2^{−α·n}
grad_var_ratio	Mean σ²_0 normalised by reference scale 2^{-n}
severity_mode	Modal plateau severity across seeds
trainability_stratum	trivial_plateau / transition_zone / robust_trainable
mean_effective_dim	Mean gradient signal persistence
mean_trainability_lifetime	Mean steps until gradient decay
mean_landscape_roughness	Mean optimization landscape roughness
mean_curvature_proxy	Mean loss surface curvature estimate

Outcome Distribution

Architecture	barren_plateau	converged	slow_convergent	stagnant
StronglyEntangling	1,406	548	1,538	8
BasicEntangler	1,448	471	1,446	135
RealAmplitudes	88	1,712	1,700	0
EfficientSU2	135	1,683	1,482	0

Benchmark Results

All results on the transition zone stratum only (61 configs where converged_rate ∈ (0, 0.5]). The transition zone is the scientifically hard stratum; unstratified evaluation inflates performance by averaging over ~70% trivially-barren configurations.

Method	Metric	Result
GP-Matern	MAE	0.121 ± 0.014
GP-Matern	AUC	0.500 ± 0.000
Quantum kernel IQP (StronglyEntangling)	AUC	0.439 ± 0.255
Quantum kernel IQP (BasicEntangler)	AUC	0.532 ± 0.206
Classical RBF SVM (StronglyEntangling)	AUC	0.432 ± 0.179
Active learning (any strategy, StronglyEntangling)	Recall@80%	< 63% within 50 queries

The transition zone is currently unpredictable by all standard methods tested. This is the open benchmark.

Usage

import pandas as pd

# Full trajectory dataset
traj = pd.read_parquet("sirius_14k_trajectories_labeled.parquet")

# Config-level summaries (best for predicting trainability)
config = pd.read_parquet("sirius_14k_config_labeled.parquet")

# Filter to transition zone (the scientifically hard regime)
tz = config[config["trainability_stratum"] == "transition_zone"]

# Separate the two failure mode profiles
gradient_barren = config[config["grad_var_scaling_exp"] > 0.7]
restricted_dla  = config[config["grad_var_scaling_exp"] < 0.5]

Architectures

All circuits implemented natively in PennyLane (default.qubit). Parameter initialisation: uniform random in [0, 2π).

• StronglyEntanglingLayers: d layers of 3-angle SU(2) rotations with multi-range two-qubit CNOT entanglement. P = 3nd parameters.
• BasicEntanglerLayers: d layers of single-angle Rx rotations with nearest-neighbour CNOT entanglement. P = nd parameters.
• RealAmplitudes: d alternating blocks of Ry rotations and linear CNOT ladders, with a final Ry layer (Qiskit convention). P = n(d+1) parameters.
• EfficientSU2: d layers of Ry/Rz rotation pairs followed by a linear CZ entanglement ladder (Qiskit convention). P = 2nd parameters.

Theoretical Context

The gradient variance scaling exponent α connects to DLA theory (Ragone et al., Nature Communications, 2024):

Var_θ[∂L/∂θ_k] = C · [dim(𝔤)]^{-1}

For full-algebra circuits (dim(𝔤) = 4^n − 1): α ≈ 1.0 (gradient-barren profile). For restricted-DLA circuits: α << 1, gradient variance above the reference scale (restricted-DLA profile).

The grad_var_ratio reference scale 2^{-n} is not the theoretical Haar-random Var_θ (which scales as O(4^{-n}) for global cost). A rigorous Haar comparison requires Var_θ measured across random initialisations and is planned for v2.

Limitations

• Noiseless simulation (noise-induced barren plateaus per Wang et al. 2021 not represented)
• Local cost function ⟨Z_0⟩ only (global cost results may differ)
• Gradient variance measured along single trajectories, not across parameter space
• n ≤ 16 qubits; α_n fits use K=7 qubit counts with no confidence intervals
• 4 hardware-efficient ansatz families; QAOA and UCC architectures not included
• EfficientSU2 uses linear CZ topology only

Citation

@article{karli2026sirius,
  title   = {{SIRIUS-14k}: A Labeled Dataset for Barren Plateau Trainability
             in Variational Quantum Algorithms},
  author  = {Karli, Derya},
  journal = {arXiv preprint},
  year    = {2026},
  url     = {https://huggingface.co/datasets/SiriusQuantum/sirius-14k}
}

Related Papers

• McClean et al. (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications.
• Ragone et al. (2024). A unified theory of barren plateaus for deep parametrized quantum circuits. Nature Communications.
• Cerezo et al. (2021). Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications.
• Holmes et al. (2022). Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum.
• Wang et al. (2021). Noise-induced barren plateaus in variational quantum algorithms. Nature Communications.
• Larocca et al. (2025). A review of barren plateaus in variational quantum computing. Nature Reviews Physics.
• Cerezo et al. (2023). Does provable absence of barren plateaus imply classical simulability? arXiv:2312.09121.

License

Apache 2.0. Dataset generated using PennyLane (Apache 2.0).