Noise-Aware Quantum Architecture Search Based on NSGA-II Algorithm

TL;DR

The paper addresses the challenge of automatically designing quantum architectures for variational quantum algorithms under hardware noise. It proposes NA-QAS, a framework that combines noise-aware training, a hybrid Hamiltonian parameter-sharing strategy with supernets, and a variable-depth NSGA-II search to identify robust PQCs. Key contributions include an explicit noise model integration for bit-flip, depolarizing, and thermal relaxation channels, a parameter-sharing mechanism to reduce evaluation overhead, and an enhanced NSGA-II capable of exploring variable-depth architectures. Empirical results on binary and iris classification under simulated noise show NA-QAS achieves higher accuracy with lower CNOT counts and circuit depths compared with baselines, highlighting potential for scalable deployment of VQAs on NISQ hardware.

Abstract

Quantum architecture search (QAS) has emerged to automate the design of high-performance quantum circuits under specific tasks and hardware constraints. We propose a noise-aware quantum architecture search (NA-QAS) framework based on variational quantum circuit design. By incorporating a noise model into the training of parameterized quantum circuits (PQCs) , the proposed framework identifies the noise-robust architectures. We introduce a hybrid Hamiltonian $\varepsilon$ -greedy strategy to optimize evaluation costs and circumvent local optima. Furthermore, an enhanced variable-depth NSGA-II algorithm is employed to navigate the vast search space, enabling an automated trade-off between architectural expressibility and quantum hardware overhead. The effectiveness of the framework is validated through binary classification and iris multi-classification tasks under a noisy condition. Compared to existing approaches, our framework can search for quantum architectures with superior performance and greater resource efficiency under a noisy condition.

Figures (6)

• Figure 1: Workflow of NA-QAS framework. In step 1, the unitary $U_f$ refers to the data encoding layer. The search space consists of two components: a rotation-gate combination space and an entanglement-gate combination space. All possible rotation-gates are highlighted by the green hexagon and entanglement-gates are highlighted by the orange hexagon. In step 2, a sampled ansatz is coupled with the noise model, and a hybrid Hamiltonian parameter-sharing strategy is added during the training process. The shared parameters are saved. In step 3, we employ a multi-objective optimization algorithm based on NSGA-II to search for the optimal ansatzes within the search space.
• Figure 2: Convergence analysis and parameter dynamics for the binary classification task. (a) Evolution of the loss function across training epochs for NA-QAS (ours) compared with random and conventional NSGA-II search methods in both noisy and noiseless scenarios. (b) Average change of trainable ansatz parameters. Top: the parameter evolution with hybrid Hamiltonian parameter-sharing optimization strategy (ours). Bottom: the parameter evolution without hybrid Hamiltonian parameter-sharing optimization strategy.
• Figure 3: Statistical distribution of accuracy for the binary classification task. (a) Performance distribution of the ansatzes found by various QAS frameworks, highlighting the superior concentration of high-accuracy solutions generated by NA-QAS. (b) Accuracy distribution across different circuit depths ($l \in [l_{\text{min}}, l_{\text{max}}]$) using NA-QAS, showing the framework’s capability to maintain high expressibility even with reduced quantum resources.
• Figure 4: Schematic representation of the optimal quantum architectures identified for the binary classification task under noisy scenarios. (a) The optimal ansatz discovered by the NA-QAS framework, characterized by the minimum CNOT count and circuit depth while achieving peak accuracy. (b) Optimal architecture from random search with optimization strategy. (c) Optimal architecture from evolutionary search without the proposed optimization strategies.
• Figure 5: Convergence analysis and parameter dynamics for the iris multi-classification task. (a) Evolution of the loss function across training epochs for NA-QAS (ours) compared with random and conventional NSGA-II search methods in both noisy and noiseless scenarios. (b) Average change of trainable ansatz parameters. Top: the parameter evolution with hybrid Hamiltonian parameter-sharing optimization strategy (ours). Bottom: the parameter evolution without hybrid Hamiltonian parameter-sharing optimization strategy.