Source-linked AI summary
Neural Predictor based Quantum Architecture Search
Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, Hong Yao
TL;DR
VQAs require task-specific parameterized circuits, while discovering a suitable ansatz remains an open challenge. This paper uses a neural predictor to guide quantum architecture search, reporting state-of-the-art VQE and QML architectures, improved search efficiency, and transfer of predictors and ansatzes to similar problems.
Problem
VQAs depend on fixed circuit ansatzes, and discovering ansatzes tailored to different tasks remains open.
Source: §I · p. 1, B. Variational Quantum Algorithms · p. 2Method
A neural predictor uses quantum-circuit structure to estimate candidate performance and guide QAS.
Source: §I · p. 1Results
Predictor-based QAS discovers state-of-the-art quantum architectures for VQE and QML tasks and improves search efficiency.
Source: §I · p. 2, §V · p. 11Takeaways & Limitations
The predictor and QAS-found ansatz can be transferred and generalized to similar problems, including problems of different sizes.
Source: §I · p. 2
Abstract
from arXiv · showhide
Variational quantum algorithms (VQAs) are widely speculated to deliver quantum advantages for practical problems under the quantum-classical hybrid computational paradigm in the near term. Both theoretical and practical developments of VQAs share many similarities with those of deep learning. For instance, a key component of VQAs is the design of task-dependent parameterized quantum circuits (PQCs) as in the case of designing a good neural architecture in deep learning. Partly inspired by the recent success of AutoML and neural architecture search (NAS), quantum architecture search (QAS) is a collection of methods devised to engineer an optimal task-specific PQC. It has been proven that QAS-designed VQAs can outperform expert-crafted VQAs under various scenarios. In this work, we propose to use a neural network based predictor as the evaluation policy for QAS. We demonstrate a neural predictor guided QAS can discover powerful PQCs, yielding state-of-the-art results for various examples from quantum simulation and quantum machine learning. Notably, neural predictor guided QAS provides a better solution than that by the random-search baseline while using an order of magnitude less of circuit evaluations. Moreover, the predictor for QAS as well as the optimal ansatz found by QAS can both be transferred and generalized to address similar problems.
I. INTRODUCTION
VQAs use task-specific parameterized quantum circuits, but discovering an ansatz suited to each task remains open. This work introduces neural-predictor-based QAS to evaluate candidate circuits and reports improved search efficiency, competitive VQE and QML architectures, and transfer to problems of different sizes.
I. INTRODUCTION
- VQAs use parameterized circuits for tasks including optimization, Hamiltonian ground-state solving, and quantum dynamics simulation.Examples include VQE, QAOA, and variational quantum machine learning.Source: §I · p. 1
- A neural predictor evaluates candidate quantum circuits from their structure within QAS, addressing the costly exploration and evaluation of many ansatzes.The authors describe this as the first predictor-based QAS framework and say it can substantially accelerate search.Source: §I · p. 1
- The predictor-based QAS achieves a dramatic search-efficiency boost over random search and discovers state-of-the-art architectures in VQE and QML tasks.The introduction characterizes the VQE and QML performance as competitive and the discovered architectures as state-of-the-art.Source: §I · p. 2
- QAS can transfer its optimal circuit structure to problems of different sizes using a protocol that combines beam search and evolutionary techniques.The transfer protocol is developed to support this transfer.Source: §I · p. 2
II. RELATED WORK
NAS faces costly architecture evaluation, with weight sharing and performance predictors among proposed strategies. VQAs likewise rely on fixed circuit ansatzes, whose limitations motivate searching for task-specific architectures.
A. Predictor based NAS
- NAS evaluation can be a computational bottleneck because each candidate network may require training from scratch; early RL-based work took thousands of GPU hours.Weight sharing reduces candidate evaluation to a forward pass, but inherited weights lack a theoretical guarantee of matching individually optimized weights.Source: A. Predictor based NAS · p. 2
- Predictor-based NAS estimates network performance from architecture structure without specifying trainable weights and can also predict metrics such as latency or FLOPs.It can be combined with weight sharing, using fitness labels obtained from a one-shot setup.Source: A. Predictor based NAS · p. 2
B. Variational Quantum Algorithms
- VQAs use fixed PQC ansatzes across tasks, but noise, barren plateaus, and reachability deficits remain challenges when the ansatz is fixed.Fixed ansatzes are often hardware-constrained or inspired by theoretical techniques such as unitary coupled clusters.Source: B. Variational Quantum Algorithms · p. 2
C. Quantum Architecture Search
Quantum architecture search seeks task-tailored circuit ansatzes that satisfy optimization and practical constraints. This work represents and samples candidate circuits through structured search spaces and generation pipelines.
C. Quantum Architecture Search
- A poorly designed ansatz may limit expressivity or entanglement, increase noise susceptibility or resource use, or produce barren plateaus; QAS searches for circuits tailored to task and constraints.Constraints can include hardware connectivity, native gates, noise models, and the training-loss landscape.Source: C. Quantum Architecture Search · p. 3
- Prior QAS methods include greedy, evolutionary, reinforcement-learning, Bayesian-optimization, one-shot, and gradient-based search, but predictor-based evaluation had not been applied to circuit design.The authors motivate predictor-based QAS by prior empirical efficiency of predictor-based NAS.Source: C. Quantum Architecture Search · p. 3
III. METHODS
- The methods section defines N as qubit count, t as the number of gate types, and n_t as the number of primitives in a circuit.These quantities establish the notation used to describe the QAS workflow.Source: §III · p. 3
A. Search space for QAS
- Candidate circuits are represented as gate-and-position tuples that are sequentially placed; commuting gates can yield multiple lists for the same ansatz.The tuple sequence defines the sampled list representation and a legitimate circuit search space.Source: A. Search space for QAS · p. 3
- Gatewise generation builds circuits gate by gate, while layerwise generation adds half-layers on even or odd qubits; both use hierarchical generation and gate-correlation enforcement.The authors contrast these structured pipelines with chaotic, often deep random circuits that are less suited to transfer across problem sizes.Source: A. Search space for QAS · p. 3
B. Representation of the quantum circuit
The paper encodes circuit structures as multichannel images for predictor input, with depth and qubits forming the spatial dimensions and gate types forming channels. The representation is bounded by a maximum depth and relies on restrictions for one-to-one circuit mapping.
B. Representation of the quantum circuit
- Circuit images use shape [#depth, #qubit, #gate types], with each candidate represented using a fixed gate count and a maximum depth cutoff D.Shallower circuits are zero-padded to D columns, while deeper circuits are excluded.Source: B. Representation of the quantum circuit · p. 4
- The image representation maps one-to-one to circuit architectures only when two-qubit gates are adjacent and symmetric.Relaxing adjacency can make qubit pairings ambiguous; asymmetric gates require additional channels.Source: B. Representation of the quantum circuit · p. 4
- For an RNN predictor, circuit depth is treated as time, with qubit and gate-type dimensions flattened into each time-step input.Figure 2 depicts circuit-image layers fed to the RNN as successive time steps.Source: B. Representation of the quantum circuit · p. 4, Figure 2 · p. 4
- The representation supports qubit-order permutation augmentation, which can create N! times more inputs to help avoid overfitting.The text notes that this assumes permutation symmetry despite the search space's adjacency restriction.Source: B. Representation of the quantum circuit · p. 4
C. Architecture of predictor model
The predictor evaluates encoded circuit architectures, with LSTM-based RNNs generally performing better than tested MLP and CNN alternatives. Training aims to make the predictor useful for search with limited labeled circuit evaluations.
C. Architecture of predictor model
- LSTM-based RNN predictors generally perform better than MLP and CNN predictors at predicting circuit fitness.The RNN processes circuit-image layers as successive time steps.Source: C. Architecture of predictor model · p. 4
- A two-stage classifier-regressor screens dense, long-tailed circuit spaces by passing only predicted good candidates to an RNN regression model.The regression model is trained only on good ansatzes.Source: C. Architecture of predictor model · p. 4
D. Training neural predictors
- In experiments, O(10^2) circuit-performance pairs are generally enough for the QAS workflow, trading dataset preparation effort against later search efficiency.More training data can improve predictor accuracy and, in turn, overall search efficiency.Source: D. Training neural predictors · p. 5
- Training labels use the minimum loss across multiple optimization runs, while repeated runs can also support predicting loss standard deviation as a trainability indicator.A large predicted standard deviation may indicate a ragged energy landscape or possible barren plateau.Source: D. Training neural predictors · p. 5
- Predictors may perform poorly on conventional ML metrics yet still improve QAS search efficiency.The text reports overfitting even with smaller networks and large dropout ratios.Source: D. Training neural predictors · p. 5
E. QAS workflow
The workflow trains a predictor on circuit-performance data, then uses it to screen sampled candidates before evaluating a small fraction from scratch. For larger systems, the transfer protocol fills in circuits and uses beam search to reduce gates while preserving a fitness threshold.
E. QAS workflow
- Phase II screens a large sample of circuits with the trained predictor and evaluates only a tiny fraction from scratch before choosing the best-fitness candidate.The two-phase workflow first generates the dataset and trains the predictor, then filters candidates.Source: Figure 3 · p. 5, E. QAS workflow · p. 5
- The current workflow uses plain random sampling, while predictor fine-tuning and genetic or Bayesian sampling are proposed as future ways to improve search efficiency.The text also suggests combining a predictor with a VAE for gradient-based search in latent space.Source: E. QAS workflow · p. 5
F. Transferability of optimal quantum ansatz
- Directly extending each gate's range to a larger system is not based on rigorous theoretical analysis and may cause a huge performance drop.This motivates testing transfer rather than assuming direct extension will retain performance.Source: F. Transferability of optimal quantum… · p. 6
- The transfer protocol fills in half-layers to make full layers, then uses beam search to remove gates while keeping fitness above a threshold.Candidates are evaluated after reductions; inherited trainable parameters allow light fine-tuning.Source: F. Transferability of optimal quantum… · p. 6
IV. RESULTS
The results section covers supervised binary classification on fashion-MNIST and ground-state-energy estimation for the transverse field Ising model. The supplied figure passage depicts a transfer workflow rather than reporting task results.
IV. RESULTS
- The main results cover fashion-MNIST binary classification and transverse field Ising model ground-state-energy estimation.Source: §IV · p. 6
- The transfer schematic starts by filling in a layerwise circuit, then reduces it through beam search with q=2 in the example.Source: Figure 4 · p. 6
- In the transfer example, light grey squares indicate absent gates in a circuit with N = 4 qubits and depth D = 3.Source: Figure 4 · p. 6
A. Quantum machine learning on classfication of fashion-MNIST
The fashion-MNIST experiment tests neural-predictor-guided QAS on binary classification and compares screened circuits with random search and a hardware-efficient baseline. QAS finds a circuit above 0.92 validation accuracy despite training the predictor only on circuits below 0.9.
A. Quantum machine learning on classfication of fashion-MNIST
- The binary fashion-MNIST task used 500 training and 500 validation images of T-shirt/top and Dress, encoded as 10-qubit amplitude-encoded states.The search used circuits with 10 qubits, 50 primitive gates, and a depth cutoff of 10.Source: A. Quantum machine learning on… · pp. 6–7
- The classifier appends an Rx layer for random measurements, feeds measured Pauli-Z features to a trainable dense layer, and jointly optimizes circuit and post-processing weights.The model is evaluated by validation accuracy after training converges.Source: A. Quantum machine learning on… · p. 7
- Circuits were trained once with an early-stop evaluation; screened candidates still required experimental training and verification of their true performance.The authors accept potentially suboptimal performance estimates to enable high-throughput screening.Source: A. Quantum machine learning on… · p. 7
- The predictor’s validation-set regression performance was around R2 = 0.71, based on 300 circuit-accuracy examples.Figure 5 presents regression performance on training and validation sets.Source: A. Quantum machine learning on… · p. 7, Figure 5 · p. 7
- Only 195 of 30,000 randomly generated circuits (0.65%) passed the predicted-accuracy threshold of 0.89 for experimental verification.The retained circuits were subsequently trained and their true accuracy tested.Source: A. Quantum machine learning on… · p. 7
- 0.924 validation accuracy is the best reported result for neural-predictor QAS, versus 0.898 for the best of 500 random-search candidates and 0.888 for the hardware-efficient ansatz with classical post-processing.The predictor was trained on only O(100) circuit candidates.Source: Figure 7 · p. 8, A. Quantum machine learning on… · p. 8
- Above 0.92 validation accuracy, the QAS-selected ansatz exceeds every training-set circuit, whose accuracy was below 0.9.The predictor was trained on suboptimal circuits yet selected a better-performing circuit.Source: A. Quantum machine learning on… · p. 8
B. Variational quantum eigensolver for transverse field Ising model
For the N = 6 TFIM, two-stage predictor screening finds low-energy circuits from a 300-circuit training set while evaluating only a small fraction of sampled candidates. The predictors and QAS-designed ansatz also transfer to different circuit sizes and a larger TFIM system.
Setup
- The VQE search uses N = 6, 36 primitive gates, depth cutoff 10, and 300 randomly selected circuits for training; its CNN and RNN predictors use error ratio as the target.The candidate circuits come equally from gatewise and layerwise pipelines; the primitive gate set is H, Rx, Ry, Rz, XX, YY, and ZZ.Source: B. Variational quantum eigensolver for… · pp. 8–9
QAS result
- Two-stage screening first uses a CNN classifier to filter varied circuits, then an RNN regressor to assess promising candidates; the CNN has precision around 0.7 and recall around 0.47.The classification threshold is 0.014; candidates predicted below 0.005 by the regression model are recommended for VQE evaluation.Source: B. Variational quantum eigensolver for… · pp. 8–9, Figure 8 · p. 9
- 20 times higher search efficiency than random search: QAS evaluates 626 of 50,000 sampled circuits and finds five with energy below −7.7, versus about 1 in 2,000 random circuits yielding an optimal candidate.The best training-set energy was −7.61694; Fig. 9 compares the energy distributions and shows QAS can match the exact ground-state energy.Source: B. Variational quantum eigensolver for… · p. 9, Figure 9 · p. 10
- The 300-circuit training set does not include the five circuits below −7.7, illustrating that the predictors screen unseen structures despite limited training data.The authors note that physics-informed circuit selection could help when training data are scarce.Source: B. Variational quantum eigensolver for… · p. 9
Transfer of the predictor
- Without retraining, the predictors screen a 42-gate p = 3 QAOA circuit trained at 36 gates and circuits with 30 gates, where the best reaches −7.7274 versus −7.46 for p = 2 QAOA.For 30-gate circuits, 360 of 100,000 are screened and three have energy below −7.7.Source: B. Variational quantum eigensolver for… · pp. 9–10
Transferability of the optimal anstaz
- For N = 10 TFIM, the transferred ansatz reaches −12.634 with 45 parameters, outperforming the p = 3 QAOA baseline; a 35-parameter, 40-unit variant reaches −12.587.The p = 3 QAOA baseline energy is −12.56758; the smaller-system ansatz is transferred and pruned with beam search.Source: B. Variational quantum eigensolver for… · p. 10
V. DISCUSSIONS
The discussion identifies ways to refine predictor-based QAS, including improved sampling and iterative predictor updates. It also points to further investigation of ansatz transfer and predictors for noise resilience or training-energy frustration.
V. DISCUSSIONS
- Future refinements include combining learned predictors with advanced sampling, iteratively updating predictors with new verification data, and using weight sharing to prepare training data faster.Evolutionary sampling is one proposed alternative to simple random search.Source: §V · p. 10
- The authors call for more systematic ansatz-transfer protocols and suggest predictors for quantum-noise resilience or frustration in the training energy landscape.These considerations may be important for establishing nontrivial quantum advantages with VQA-based approaches in the NISQ era.Source: §V · pp. 10–11
Conclusion
- The conclusion reports improved search efficiency and new state-of-the-art quantum architectures across VQE and QML examples.The work uses neural predictors as the evaluation policy for QAS.Source: §V · p. 11
A. More details on search space design
The sampling pipelines define both the legal circuit search space and how circuits are distributed within it. The appendix also identifies the predictor models used in the QAS pipeline.
A. More details on search space design
- Gatewise generation restricts two-qubit gates to neighboring qubits on a ring and correlates successive gate choices to favor structured circuits.Gate-type logits are sampled from a Gaussian with standard deviation 1.35, with single-qubit gate logits increased by 0.5.Source: A. More details on search space design · p. 15
- Layerwise generation adds half-layers on even or odd qubits, and its sampling probabilities can be biased toward architectures required by known physical constraints.The example ZZ, Rz-odd, YY-even denotes gates applied across all sites or the specified odd or even sites.Source: A. More details on search space design · p. 15
- A search space with very rare optimal circuits can remain impractical: predictor-based QAS may need 10^6–10^7 evaluations when optimal circuits occur at probability 10^-8.In the TFIM VQE example, circuits with ε < 0.0035 occur with probability around 1/2000, despite a larger probability of sampling circuits with ε < 0.014.Source: A. More details on search space design · p. 15
B. Neural architecture for predictor models
- The predictor pipeline uses a CNN for first-stage classification and an LSTM-based RNN for second-stage regression, with qubit-order permutation as data augmentation.The illustrated input shape [10, 6, 7] corresponds to N = 6, D = 10, and seven gate types in the VQE task.Source: B. Neural architecture for predictor… · p. 15, Figure S2 · p. 17