QNAS: A Neural Architecture Search Framework for Accurate and Efficient Quantum Neural Networks

Kooshan Maleki; Alberto Marchisio; Muhammad Shafique

quant-phApr 8, 2026

QNAS: A Neural Architecture Search Framework for Accurate and Efficient Quantum Neural Networks

Authors: Kooshan Maleki, Alberto Marchisio, Muhammad Shafique

Organizations: Department of Computer Engineering, Amirkabir University of Technology, Tehran, Iran · eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE · Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, UAE

Abstract

Designing quantum neural networks (QNNs) that are both accurate and deployable on NISQ hardware is challenging. Handcrafted ansatze must balance expressivity, trainability, and resource use, while limited qubits often necessitate circuit cutting. Existing quantum architecture search methods primarily optimize accuracy while only heuristically controlling quantum and mostly ignore the exponential overhead of circuit cutting. We introduce QNAS, a neural architecture search framework that unifies hardware aware evaluation, multi objective optimization, and cutting overhead awareness for hybrid quantum classical neural networks (HQNNs). QNAS trains a shared parameter SuperCircuit and uses NSGA-II to optimize three objectives jointly: (i) validation error, (ii) a runtime cost proxy measuring wall clock evaluation time, and (iii) the estimated number of subcircuits under a target qubit budget. QNAS evaluates candidate HQNNs under a few epochs of training and discovers clear Pareto fronts that reveal tradeoffs between accuracy, efficiency, and cutting overhead. Across MNIST, Fashion-MNIST, and Iris benchmarks, we observe that embedding type and CNOT mode selection significantly impact both accuracy and efficiency, with angle-y embedding and sparse entangling patterns outperforming other configurations on image datasets, and amplitude embedding excelling on tabular data (Iris). On MNIST, the best architecture achieves 97.16% test accuracy with a compact 8 qubit, 2 layer circuit; on the more challenging Fashion-MNIST, 87.38% with a 5 qubit, 2 layer circuit; and on Iris, 100% validation accuracy with a 4 qubit, 2 layer circuit. QNAS surfaces these design insights automatically during search, guiding practitioners toward architectures that balance accuracy, resource efficiency, and practical deployability on current hardware.

Figures & tables

Panel of Figure 1 — Fig. 1 : Comparison of QAS without F3 versus with F3 on MNIST: (a) Bar chart showing average number of cuts (for $Q_{\text{target}}{=}4$ ) across 5% accuracy bins (solutions with accuracy $\geq$ 65%). (b) Cumulative distribution function (CDF) of circuit cost (F2) showing percentage of solutions with F2 $\leq$ x. The “With F3” approach reduces both cutting overhead and circuit cost while maintaining similar accuracy.

Fig. 3 : Hybrid quantum classical neural network used in QNAS.

Fig. 4 : NAS pipeline. Data and objectives feed a NAS engine that evolves DNN architectures via a supernet and accuracy predictor.

Fig. 5 : QNAS pipeline with NSGA-II. See Sec. III for details.

Fig. 6 : QNAS search space parameters and ranges. Each candidate architecture is encoded as a genome vector specifying six parameter groups: embedding type, qubit count, circuit depth, entanglement range, CNOT mode, and learning rate.

Panel of Figure 7 — Fig. 8 : CNOT mode patterns for a 4 qubit circuit with entanglement range $r{=}1$ . All : every qubit controls its neighbor. Odd : only odd indexed qubits (1, 3) act as controls. Even : only even indexed qubits (0, 2) act as controls. None : no entangling gates (product state). The mode choice significantly impacts trainability and accuracy (see Sec. V-A ).

Fig. 9 : NSGA-II selection mechanism. Left : Parent population

P_{t}

. Middle : Combined population

P_{t}\cup Q_{t}

sorted into non dominated fronts (darker = better front). Right : Selection of

P_{t+1}

from top fronts; the dashed line indicates where crowding distance breaks ties within a partially selected front.

Fig. 10 : Correlation between checkpoint accuracy and final (epoch 10) accuracy on MNIST using the full 60,000 training set. The dashed line marks

r{=}0.8

(“strong” correlation). By epoch 2, correlations exceed 0.9, validating short training budgets during search.

Parameter	Range
Embedding type	angle- $X$ , angle- $Y$ , angle- $Z$ , amplitude
Qubits $n$	$[2,8]$
Depth $L$	$[1,4]$
Entanglement range $r$ (per layer)	$[1,n{-}1]$
CNOT mode (per layer)	all, odd, even, none
Learning rate $\eta$	$[10^{-3},5{\times}10^{-3}]$

TABLE I : MNIST search space configuration.

Metric	Value	Metric	Value
Total evaluations	72	Best search val accuracy (%)	94.80
Generations	6	Best final test accuracy (%)	97.16
Training epochs/eval	2	Mean $\pm$ std accuracy (%)	51.32 $\pm$ 29.84
$Q_{\text{target}}$ (qubits)	4	Mean $F_{2}$ (s/sample)	0.070
Total search time (h)	71.19

TABLE II : MNIST search phase summary.

Fig. 11 : Pareto tradeoff between validation accuracy and runtime cost ( $F_{2}$ ). The star marks the best accuracy (94.80%).

	EvalID	Gen	Embed	Qubits	Depth	CNOT Mode	ValAcc(%)	$F_{2}$ (s/samp)	$F_{3}$
Top accuracy configurations
$\bullet$	45	4	angle-y	8	2	none-odd	94.80	0.0150	5
	51	5	angle-y	8	2	none-odd	94.17	0.0151	5
	70	6	angle-y	8	2	none-odd	93.24	0.0152	5
$\bullet$	49	5	angle-y	5	2	none-odd	93.12	0.1238	4
	66	6	angle-y	8	1	odd	92.65	0.1409	4

TABLE III : Search results: top configurations by accuracy and Pareto optimal solutions. Rows marked

\bullet

are Pareto optimal over

(F_{1},F_{2},F_{3})

; unmarked rows are top accuracy configurations. Angle-y with CNOT mode “none-odd” dominates both categories.

Fig. 12 : Training dynamics during 12 epoch retraining on full MNIST for three Pareto optimal architectures: Balanced (96.83% accuracy), Best Accuracy (97.16%), and Lowest Cost (87.84%). All configurations use angle-y embedding with CNOT mode “none-odd”. Loss (left axis) and accuracy (right axis) are shown for both training and validation sets.

Fig. 13 : Number of subcircuits ( $F_{3}$ ) versus qubit count for $Q_{\text{target}}{=}4$ . Since cutting overhead scales as $\mathcal{O}(4^{k})$ per cut, minimizing $F_{3}$ is critical.

Config	Depth		CNOTs		Gates		CNOT
	Pre	Post	Pre	Post	Pre	Post	Mode
8q-2d (Best Acc.)	10	14	4	4	68	68	none-odd
5q-2d (Balanced)	9	12	2	2	42	42	none-odd
4q-2d (Low Cost)	9	12	2	2	34	36	none-odd

TABLE IV : Transpilation analysis for Pareto optimal architectures. Circuits transpiled to fake_melbourne (15q) with optimization level 3. Sparse CNOT modes yield minimal routing overhead.

Panel of Figure 17 — Fig. 14 : Transpiled 8 qubit angle-y circuit (CNOT mode “none-odd”) on fake_melbourne with global phase $\pi$ . The transpiler decomposes rotations into the native basis $\{R_{z},\sqrt{X}\}$ . The mapping $q_{i}\mapsto j$ shows logical to physical qubit assignment.

Metric	Value	Metric	Value
Total evaluations	66	Best search val accuracy (%)	83.28
Generations	6	Best final test accuracy (%)	87.38
Training epochs/eval	2	Mean $\pm$ std accuracy (%)	52.91 $\pm$ 26.47
$Q_{\text{target}}$ (qubits)	4	Mean $F_{2}$ (s/sample)	0.066
Total search time (h)	65.51

TABLE V : Fashion-MNIST search phase summary.

	EvalID	Gen	Embed	Qubits	Depth	CNOT Mode	ValAcc(%)	$F_{2}$ (s/samp)	$F_{3}$
Top accuracy configurations
$\bullet$	31	3	angle-y	5	2	none-none	83.28	0.0694	3
	63	6	angle-x	5	1	none	81.88	0.0805	2
$\bullet$	47	5	angle-y	8	4	none-none-odd-odd	80.15	0.0258	12
	67	6	angle-y	5	2	none-none	80.13	0.1158	3
$\bullet$	22	2	angle-y	6	1	even	79.74	0.0075	2

TABLE VI : Fashion-MNIST search results: top configurations by accuracy and Pareto optimal solutions. Angle-y embedding dominates across all top performers.

Parameter	Range
Embedding type	angle- $X$ , angle- $Y$ , angle- $Z$ , amplitude
Qubits $n$	$[2,8]$
Depth $L$	$[1,5]$
Entanglement range $r$ (per layer)	$[1,n{-}1]$
CNOT mode (per layer)	all, odd, even, none
Learning rate $\eta$	$[10^{-3},5{\times}10^{-3}]$

TABLE VII : Iris search space configuration.

Metric	Value	Metric	Value
Total evaluations	120	Best search val accuracy (%)	100.00
Generations	10	Best final val accuracy (%)	100.00
Training epochs/eval	5	Mean $\pm$ std accuracy (%)	66.67 $\pm$ 28.19
$Q_{\text{target}}$ (qubits)	2	Mean $F_{2}$ (s/sample)	0.121
Total search time (h)	0.60

TABLE VIII : Iris search phase summary.

	EvalID	Gen	Embed	Qubits	Depth	CNOT Mode	ValAcc(%)	$F_{2}$ (s/samp)	$F_{3}$
Top accuracy configurations
$\bullet$	62	5	amplitude	4	2	none-odd	100.00	0.0070	6
$\bullet$	104	8	amplitude	2	2	odd-all	100.00	0.0634	1
	48	3	amplitude	4	2	none-even	100.00	0.0395	6
	71	5	amplitude	4	2	none-even	100.00	0.0373	6
$\bullet$	74	6	amplitude	4	1	odd	100.00	0.0256	4

TABLE IX : Iris search results: top configurations by accuracy and selected Pareto optimal solutions. Amplitude embedding dominates; best accuracy is 4q-2d with none-odd.

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Hybrid Quantum-Classical Neural Architecture Search

Alberto Marchisio, Muhammad Kashif, Nouhaila Innan, Muhammad Shafique

eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, United Arab Emirates · Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, United Arab Emirates

Quantum Machine Learning Hybrid Quantum-Classical ML Hardware-Aware NAS Neural Architecture Search Quantum Neural Networks Quantum Architecture Search

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Hybrid quantum-classical neural networks (HQNNs) are emerging as a practical approach for quantum machine learning in the noisy intermediate-scale quantum (NISQ) era, as they combine classical learning components with parameterized quantum circuits in an end-to-end trainable framework. However, their performance and efficiency depend strongly on architectural choices such as data encoding, circuit structure, measurement design, and the coupling between classical and quantum modules. This makes manual design increasingly difficult, especially when hardware limitations and resource constraints must also be taken into account. In this paper, we study the foundations of HQNNs and neural architecture search (NAS), discuss how NAS extends to quantum and hybrid settings, and demonstrate FLOPs-aware search (where FLOPs serve as a proxy for computational complexity), as an important hardware-aware direction for building HQNNs that are not only accurate but also computationally efficient and practically deployable.

Abstract

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