Noise-aware variational quantum classifier training
Domain: quantum (ai-for-quantum, noisy-quantum-training, robustness)
Topic: Noise-aware variational quantum classifier training: comparing training under simulated depolarizing noise vs ideal-statevector training, evaluating both robustness to test-time noise and clean-test transfer
Venue: ARC-Bench 2026
Headline metric: test_accuracy (maximize)

Research briefing:
Real quantum hardware exhibits gate errors, readout errors, and
decoherence at rates that vary across devices. A VQC trained on a
noiseless statevector simulator may converge to parameters that work
on the ideal training distribution but degrade sharply when deployed
on a noisy device. The noise-aware training strategy is to inject
simulated noise during training (e.g. a depolarizing channel after
each two-qubit gate) so the optimizer can find parameters that are
robust to that noise model. The closest classical analog is
adversarial training or training-time data augmentation.

Two open empirical questions follow. First, does noise-aware training
produce strictly more robust models on noisy test data than ideal
training, and at what training noise rate is the robustness gain
worth the loss of clean-test accuracy? Second, does training at high
noise (p=0.01) cause negative transfer to clean test data — i.e.
does the model overfit to the noise statistics and underperform an
ideal-trained model on noise-free evaluation? Wang et al. (NeurIPS
2022 "QuantumNAS: Noise-Adaptive Search for Robust Quantum
Circuits") and Sharma et al. (PRX Quantum 2022 "Trainability of
dissipative perceptron-based quantum neural networks") explored
these tradeoffs at small scale, leaving the precise sweet-spot
noise rate as a benchmark question.

Implementation guidance is provided by the quantum-qiskit skill at
stage 10. Use qiskit_aer.AerSimulator with a custom NoiseModel that
applies a single-qubit and two-qubit depolarizing channel after each
parameterized gate. The training uses
qiskit_machine_learning.algorithms.VQC with a custom
qiskit.primitives.BackendSamplerV2 bound to the noisy AerSimulator
for noisy-train conditions, and the noiseless reference
qiskit.primitives.StatevectorSampler for the ideal-train condition.
Evaluation always runs on both an ideal statevector test set and a
noisy test set at p=0.01 (the "deployment noise rate") so each cell
produces two test_accuracy values: clean and noisy. The primary
metric is the average across both.

Experimental protocol. Four quantum training conditions vary the
training noise rate: ideal (p=0), low noise (p=0.001), mid noise
(p=0.005), high noise (p=0.01). Two baselines complete the bench
gate: a no-training control (random initialization, no fit) and
logistic regression on the same 4D features. All six conditions
are evaluated on a single synthetic binary classification dataset
(make_classification with class_sep=0.5, 200 samples, 4 features),
averaged over 3 seeds. Total: 6 conditions x 1 dataset x 3 seeds
= 18 cells.

Research question: *On a synthetic 4D binary classification task,
does noise-aware VQC training at a moderate training noise rate
(p=0.005) produce a model that is more robust to test-time
depolarizing noise (p=0.01) than an ideal-trained VQC, and does
high training noise (p=0.01) cause negative transfer to clean
test data?*

Hypotheses:
statement: On the noisy test set at p=0.01, the noisy-trained-mid VQC (training noise p=0.005) achieves test accuracy at least 5 absolute percentage points higher than the ideal-trained VQC (3-seed mean), demonstrating that moderate noise-aware training improves test-time noise robustness., statement: On the ideal test set (noiseless), the ideal-trained VQC outperforms every noisy-trained variant by at least 2 absolute percentage points (3-seed mean), reflecting the no-free-lunch tradeoff that noise-aware training sacrifices some clean-test accuracy., statement: The high-noise-trained VQC (training noise p=0.01) performs worse than the mid-noise-trained VQC on BOTH clean and noisy test sets (3-seed mean), indicating that p=0.01 is past the sweet spot and the optimizer is overfitting to noise statistics — negative transfer.

Experiment design:
research_question: Does noise-aware VQC training at a moderate training noise rate (p=0.005) produce a model more robust to test-time depolarizing noise than ideal training, and does high training noise cause negative transfer on clean test data?
conditions: name: train_ideal
description: VQC trained on noiseless qiskit.primitives.StatevectorSampler. EfficientSU2(num_qubits=4, reps=2, entanglement='linear') ansatz + ZFeatureMap feature map. qiskit_machine_learning.VQC(optimizer=COBYLA(maxiter=200), sampler=StatevectorSampler()). After training, evaluate on BOTH ideal test (StatevectorSampler) and noisy test (depolarizing p=0.01 NoiseModel)., name: train_noisy_low
description: Same ansatz + feature map. VQC trained on a noisy AerSimulator with depolarizing channel p=0.001 applied after every single-qubit and two-qubit gate. Same COBYLA maxiter=200. Evaluate on both ideal and noisy test sets., name: train_noisy_mid
description: Same as train_noisy_low but training noise rate p=0.005., name: train_noisy_high
description: Same as train_noisy_low but training noise rate p=0.01 (matches the test-noise rate).
baselines: no_training_control: Same ansatz but parameters randomly initialized and never trained. Evaluate predict() directly on both test sets. Establishes the untrained floor., logistic_regression: sklearn.linear_model.LogisticRegression(max_iter=1000, random_state=seed) on the same 4 features. Classical baseline.
metrics: name: test_accuracy
direction: maximize
description: Average of test_accuracy_ideal and test_accuracy_noisy_p01, 3-seed mean. Primary metric for the bench., name: test_accuracy_ideal
direction: maximize
description: Test accuracy on the noiseless test set (StatevectorSampler evaluation), 3-seed mean., name: test_accuracy_noisy_p01
direction: maximize
description: Test accuracy on the noisy test set at depolarizing rate p=0.01 (AerSimulator with NoiseModel), 3-seed mean. The 'deployment-noise' robustness metric.
datasets: name: synthetic_classification_4d_sep05
source: sklearn.datasets.make_classification
description: make_classification(n_samples=200, n_features=4, n_informative=3, n_redundant=0, n_clusters_per_class=1, class_sep=0.5, flip_y=0.05, random_state=seed). Moderately difficult binary classification, native 4D. StandardScaler fit on train only. 80/20 split.
compute_requirements: gpu_required: no
estimated_wall_clock_sec: 1500

Requirements:

Scoring rubric:
requirements: An empirical study of noise-aware VQC training. Four quantum training conditions vary the training-time depolarizing noise rate (ideal, p=0.001, p=0.005, p=0.01), evaluated on both an ideal test set and a noisy test set at p=0.01. The agent must (a) implement the noise model via qiskit_aer.NoiseModel applying single-qubit and two-qubit depolarizing channels, (b) train VQC under each noise level using qiskit_machine_learning.VQC with the appropriate sampler, (c) evaluate each trained model on BOTH ideal and noisy test sets to expose the robustness-vs-clean-accuracy tradeoff, and (d) score H1/H2/H3 with numerical evidence.
judging_note: Noise-aware training studies are scored on (i) correctness of the qiskit_aer NoiseModel construction (depolarizing channel must be applied after every gate, not only after measurement; verifiable by inspecting the agent's noise model setup), (ii) test_accuracy reporting BOTH ideal and noisy variants per cell (without both, H1 cannot be evaluated), (iii) the noise-rate sweep producing visibly different test accuracies (cells reporting identical numbers across noise levels indicate the noise model is not actually being applied during training), and (iv) numerical evidence backing the three-way comparison: ideal-train vs noisy-mid-train vs noisy-high-train.
sub_tasks: requirements: Code-development bucket: NoiseModel correctly constructed, training pipeline applies noise, evaluation on both ideal and noisy test.
sub_tasks: requirements: qiskit_aer.NoiseModel with depolarizing_error applied to all single-qubit gates (h, ry, rz, etc.) AND two-qubit gates (cx). For a noisy-train condition at rate p, the single-qubit error rate is p and the two-qubit error rate is p (or some agent-documented scaling of p). A sanity check verifies that the same ansatz parameters produce different expectation values under the noise model vs under StatevectorSampler (otherwise the noise is not being applied).
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: Each training condition uses qiskit_machine_learning.VQC with a qiskit.primitives.BackendSamplerV2 (or BackendSampler) bound to either AerSimulator (for noisy training) or StatevectorSampler (for ideal training). Same ansatz family (EfficientSU2 num_qubits=4 reps=2 entanglement='linear'), same optimizer (COBYLA maxiter=200), same per-seed random initialization across noise-rate conditions for paired comparison.
task_category: Code Development
finegrained_task_category: Experimental Setup, requirements: Each trained VQC is evaluated on TWO test sets: (a) ideal StatevectorSampler (test_accuracy_ideal), (b) noisy AerSimulator at depolarizing p=0.01 (test_accuracy_noisy_p01). Both numbers are logged per cell. The primary 'test_accuracy' metric is the average of the two. Each cell's METRIC_RESULT JSON includes all three numbers.
task_category: Code Development
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Execution-validity bucket: all 18 cells ran with valid outputs.
sub_tasks: requirements: At least 16 cells out of 18 expected (6 conditions x 1 dataset x 3 seeds) completed without unhandled errors and produced both test_accuracy_ideal AND test_accuracy_noisy_p01 values. Missing more than 2 cells (10 percent) without documented justification fails this leaf.
task_category: Code Execution
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Numerical validity: both test accuracies in [0, 1]; for any single training condition, test_accuracy_ideal and test_accuracy_noisy_p01 differ by at least 0.01 (cells reporting bit-identical clean and noisy accuracy mean the noise model isn't being applied at evaluation); no_training_control accuracy is in [0.4, 0.6] (random predictor floor).
task_category: Code Execution
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Results bucket: quantitative tests of H1/H2/H3 plus a per-hypothesis writeup.
sub_tasks: requirements: Quantitative test of H1. On the noisy test set at p=0.01, is train_noisy_mid (training noise p=0.005) test_accuracy >= train_ideal test_accuracy + 5 absolute pp (3-seed mean)? 100% if gap >= 5pp, 67% if 2-5pp, 33% if any positive gap, 0% if ideal train matches or beats noisy-mid train on noisy test.
task_category: Result Analysis
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Quantitative test of H2. On the ideal test set, does train_ideal beat EVERY noisy-trained variant by >= 2 absolute pp (3-seed mean)? 100% if gap >= 2pp vs all three noisy variants, 67% if gap >= 2pp vs at least 2 of 3, 33% if marginal advantage on at least 1, 0% if noisy training matches or beats ideal training on clean test (no tradeoff).
task_category: Result Analysis
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Quantitative test of H3. Does train_noisy_high underperform train_noisy_mid on BOTH the clean and the noisy test set (3-seed mean)? 100% if cleanly worse on both, 67% if worse on 1 of 2 by >= 3pp, 33% if marginally worse on 1, 0% if high-noise training matches or beats mid-noise on both test sets (no negative transfer observed).
task_category: Result Analysis
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Writeup of at least 200 words (submission/README.md ## Agent-produced writeup section) with explicit supported / refuted / inconclusive verdict for each of H1/H2/H3 backed by per-(training_noise_rate, test_set) 3-seed mean accuracy values. References Wang NeurIPS 2022 QuantumNAS and Sharma PRX Quantum 2022. Discusses whether the observed sweet-spot noise rate matches the test-deployment rate, and acknowledges that AerSimulator depolarizing channel is a simplified model relative to real hardware noise (T1/T2, crosstalk, readout asymmetry not captured).
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation