QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits

• NISQ devices have error rates of 10^-3 to 10^-2, making quantum-error reduction necessary to bridge algorithmic demands and available hardware.Source: §I · p. 1
• Existing noise-adaptive methods mainly optimize compilation components such as qubit mapping, scheduling, and crosstalk, leaving circuit-level co-design less explored.Source: §I · pp. 1–2
• QuantumNAS targets a task and device by jointly searching a robust variational circuit and its corresponding qubit mapping with noise information in the loop.Source: §I · p. 2
• On MNIST-4, increasing parameters improves noise-free accuracy but can reduce measured accuracy because additional gates accumulate noise; circuit choice also creates large variance.Source: §I · p. 2, Figure 2 · p. 2
• A SuperCircuit shares gates across many SubCircuits, allowing one training process to estimate SubCircuit performance before evolutionary co-search evaluates circuit–mapping pairs under device noise.Source: Figure 1 · p. 1, §I · p. 2
• Iterative pruning and finetuning remove redundant gates while preserving noise-free performance, yielding fewer noise sources and improved measured performance.Source: §I · pp. 2–3

Motivation

• Quantum circuits must balance expressive capacity against noise, because additional parameters introduce more gates and can offset accuracy gains.In the MNIST motivation, measured accuracy peaks at 45 parameters as accumulated noise offsets the capacity benefit.Source: A. Quantum Basics · p. 3

Variational Quantum Circuits

• Variational circuits use parameterized gates whose trainable parameters are optimized for computational tasks such as QML and VQE.QML circuits encode inputs, process them with trainable gates, and measure qubits; VQE circuits prepare states for molecular-energy estimation.Source: B. Variational Quantum Circuits · p. 3

Noise-Adaptive Search

• Evolutionary search mutates and recombines SubCircuit–qubit-mapping pairs, while later pruning removes redundant gates before deployment.The broader workflow evaluates candidates, searches for the best pair, trains the selected SubCircuit, prunes gates, finetunes, and compiles for real devices.Source: A. Overview · p. 4, Figure 5 · p. 4

SuperCircuit Construction and Training

• SuperCircuit represents a large gate design space and trains sampled SubCircuits by updating only their selected parameters.A SubCircuit can vary in its number of blocks and gates, while the SuperCircuit contains the full gate set.Source: B. SuperCircuit Construction and… · p. 4, Figure 6 · p. 5

Efficient Search

• Inherited SuperCircuit parameters provide relative SubCircuit performance estimates without fully training every candidate, reducing search cost.Relative performance is sufficient for derivative-free evolutionary search, and the reported reduction is around N_device × N_search, or 16,000 in the stated setting.Source: B. SuperCircuit Construction and… · pp. 4–5

SuperCircuit Construction and Training

• Front sampling and restricted sampling address sampling variance by improving parameter sharing and limiting changes between successive SubCircuits.Restricted sampling constrains the maximum number of differing layers; the illustrated example limits differences to 3 layers instead of 5.Source: B. SuperCircuit Construction and… · p. 5, Figure 7 · p. 5

• The genetic search encodes circuit width, depth, and logical-to-physical qubit mapping in a joint candidate representation.Source: C. Noise-Adaptive Evolutionary Co-Search · p. 5
• Each iteration evaluates candidate pairs, selects high-performing parents, and generates new populations through mutation and crossover.Source: C. Noise-Adaptive Evolutionary Co-Search · p. 6
• The performance estimator inherits SuperCircuit parameters and evaluates candidates using noise-aware simulation or real quantum hardware.Source: C. Noise-Adaptive Evolutionary Co-Search · p. 6
• The estimator switches between a more accurate slower method and a faster less accurate method, using the former for circuits with ≤10 qubits.Source: C. Noise-Adaptive Evolutionary Co-Search · p. 6
• The estimator’s two approximations retain useful relative-ranking reliability, with average Spearman correlation 0.75 across five tasks and two design spaces.Source: C. Noise-Adaptive Evolutionary Co-Search · p. 6

• Iterative pruning targets redundant parameters and gates left by evolutionary search or unnecessary among similarly performing parameter sets.Source: D. Iterative Quantum Pruning · p. 6
• The method ranks normalized rotation angles and removes those closest to 0°, then finetunes the remaining parameters to recover accuracy.Source: D. Iterative Quantum Pruning · p. 6
• Pruning ratios increase iteratively until the desired final ratio is reached, using polynomial pruning-ratio decay.Source: D. Iterative Quantum Pruning · p. 7
• The final ratio preserves noise-free simulation performance relative to the unpruned circuit, while fewer compiled gates can increase accuracy by up to 9%.Source: D. Iterative Quantum Pruning · p. 7

• TorchQuantum implements quantum states and gate matrices with native torch.Tensor objects for differentiable circuit simulation.Source: E. TorchQuantum Library · p. 7
• The library supports common quantum gates, PyTorch-style APIs, IBM Qiskit conversion, ready-to-use templates, and parameter-shift gradients.Source: E. TorchQuantum Library · p. 7
• TorchQuantum uses tensorized CPU/GPU batch processing, avoiding PennyLane’s linear training-speed reduction with batch size.Source: E. TorchQuantum Library · p. 7
• 246 to 104 times faster training was measured for 10-qubit circuits containing 100 RX and 100 CRY gates versus PennyLane.Source: E. TorchQuantum Library · p. 7
• The evaluation covers 6 QML and 6 VQE tasks across IBM quantum devices, with reported experiments using device-specific configurations and baselines.Source: A. Evaluation Methodology · pp. 7–8
• QuantumNAS achieves the highest accuracy on real QC devices in Figure 13, with pruning improving accuracy by 2% on average.Source: Figure 13 · p. 9
• On four 5-qubit real QC devices, QuantumNAS designs outperform baseline designs with higher measured accuracy.Source: Figure 14 · p. 9

QML results

• Over 85% 4-class and 95% 2-class accuracy was achieved on IBMQ-Yorktown across five QML tasks, generally outperforming baselines.Pruning improved average accuracy by 2% for 4-class and 1% for 2-class tasks.Source: B. Experimental Results · p. 9
• 3% accuracy improvement accompanied pruning that removed 14 parameters and reduced circuit depth by 11.The pruned circuit retained similar noise-free accuracy while using fewer gates and experiencing less noise.Source: B. Experimental Results · p. 9

Device variation

• 5% better average accuracy was obtained on IBMQ-Santiago than baselines despite its lower noise.Performance remained much higher than baselines three weeks after search, supporting device-specific noise adaptation.Source: B. Experimental Results · p. 9
• Best performance occurred when circuits were searched and run on the same device, demonstrating the value of device-specific circuits.QuantumNAS used noise models tailored to each target device.Source: B. Experimental Results · pp. 9–10

Scalability

• QuantumNAS achieved over 5% better accuracy for a 21-qubit model and supports training, search, and evaluation on quantum machines.Real-QC training with parameter shift produced accuracy comparable to classical-simulator training, while runtime increased approximately linearly with qubit count.Source: B. Experimental Results · p. 10

VQE results

• QuantumNAS consistently produced lower H2 expectation values than baselines, while pruning 50% of parameters steadily reduced eigenvalues.The theoretical optimal value for H2 is -1.85, and UCCSD was far from optimal under hardware noise.Source: B. Experimental Results · pp. 10–11, Figure 17 · p. 11, Figure 18 · p. 11

Search components

• 9% average accuracy gain came from co-designing circuit structure and qubit mapping, exceeding either noise-adaptive search alone.Circuit search alone improved accuracy more than mapping search alone because its design space is larger.Source: C. Performance Analysis · p. 11, Figure 19 · p. 11
• 12% higher final accuracy was achieved with front and restricted sampling than with random sampling.These strategies control differences between consecutive samples, stabilizing SuperCircuit training and improving relative-performance estimates.Source: C. Performance Analysis · p. 11, Figure 20 · p. 11

Hardware effects

• Lower device error rates improve performance under the same topology, while topology and mapping also affect results.These observations motivate hardware-aware design and mapping choices.Source: C. Performance Analysis · p. 11, Figure 21 · p. 12

Design space

• Larger design spaces can outperform shallow circuits because QuantumNAS balances learning capacity against noise.Small U3+CU3 spaces had consistently worse accuracy despite lower circuit noise.Source: C. Performance Analysis · pp. 11–12, Table VI · p. 12

Search components

• Evolutionary search found lower-loss SubCircuit–mapping pairs than random search, whose best performance quickly saturated.The lower-loss pairs delivered higher accuracy.Source: C. Performance Analysis · p. 12, Figure 22 · p. 12

Pruning

• A pruning sweet spot maximizes accuracy by balancing gate-error reduction against reduced circuit capacity.Circuits with more parameters generally tolerate larger pruning ratios.Source: C. Performance Analysis · p. 12, Figure 23 · p. 12, Table VII · p. 13

Conclusion

• QuantumNAS is a noise-adaptive co-search framework for robust variational circuits and qubit mappings.It uses SuperCircuit-based search to explore a broad design space and iterative pruning to remove redundant gates.Source: §VI · p. 13
• Experiments on QML and VQE tasks demonstrate higher robustness and performance than baseline designs.The conclusion positions the framework as applicable across both machine-learning and quantum-simulation workloads.Source: §VI · p. 13
• TorchQuantum is open-source infrastructure for fast training of parameterized quantum circuits and future variational-algorithm research.Source data is also planned for release to facilitate further research.Source: §VI · p. 13

Outlook

• Future directions include noise-adaptive quantum feature-map design, barren-plateau mitigation, and chemistry applications of ansatz search.These directions are presented as opportunities for further theoretical and experimental exploration.Source: §VI · p. 13

• QuantumNAS searches for a robust parameterized-circuit architecture and corresponding qubit mapping with noise information in the loop.Source: A. Abstract · p. 13
• TorchQuantum supports parameterized quantum-circuit research, while the QuantumNAS pipeline covers SuperCircuit training, search, SubCircuit training, pruning, and real-hardware evaluation.Source: A. Abstract · p. 13

Benchmarks

• The artifact includes QNN image classification, vowel recognition, and VQE benchmarks using automatically searched and human-designed models.Source: B. Artifact check-list… · p. 14

Requirements and availability

• The artifact is publicly available under the MIT License and uses Python, PyTorch, Qiskit, Intel CPUs, Nvidia GPUs, and remote IBMQ access.Source: B. Artifact check-list… · p. 14

Runtime conditions

• Real-machine noise changes constantly, and one 4-qubit circuit search and test takes approximately 5 to 10 CPU hours or 5 to 10 times less on one Nvidia GPU.Source: B. Artifact check-list… · p. 14

Metrics

• Classification uses top1 accuracy, whereas VQE uses molecule ground-state expectation value, with higher classification accuracy and lower VQE energy preferred.Source: B. Artifact check-list… · p. 14

Access and hardware

• The artifact is available at the TorchQuantum GitHub repository, with remote IBMQ access required and a GPU highly recommended for faster training.Source: 2) Hardware dependencies · p. 14

Software

• The software dependencies include Python, PyTorch, Qiskit, and the packages listed in requirements.txt.Source: 3) Software dependencies · p. 14

Datasets and benchmarks

• Datasets include Vowel recognition, MNIST, and FashionMNIST, while VQE benchmarks cover various molecules.Source: 4) Data sets · p. 14

Models and baselines

• QNN models are searched SubCircuits, with human design, random search, and noise-unaware searched models used as baselines.Source: 5) Models · p. 14

Installation

• The repository can be installed locally with `pip install --editable .`, with detailed instructions provided in README.md.Source: D. Installation · p. 14

TorchQuantum example

• The artifact provides examples for constructing, training, and deploying a simple MNIST QNN through `./example1/1_train_qnn.sh`.Source: E. Experiment workflow · p. 14, 1) Running the TorchQuantum library · p. 15

QuantumNAS pipeline

• The QuantumNAS workflow runs SuperCircuit training, co-search, SubCircuit training, pruning, and evaluation through five documented scripts.Source: §I · p. 15

Baselines

• Separate scripts train and evaluate human baseline designs, and additional scripts cover datasets, design spaces, quantum machines, and other baselines.Source: §I · p. 15

Training functionality

• Successful circuit training should produce decreasing classification loss and increasing training accuracy.Source: F. Evaluation and expected results · p. 15

Expected results

• QuantumNAS is expected to achieve better classification accuracy and lower molecule ground-state energy expectation values than baseline models.Source: F. Evaluation and expected results · p. 15

General framework

• TorchQuantum supports constructing, training, and deploying customized quantum-circuit architectures from scratch.Source: G. Experiment customization · p. 15

Reproducibility boundary

• Several IBMQ machines used for the paper’s real-device results, including Yorktown, Athens, and Melbourne, have already retired.Source: H. Notes · p. 15