QaML: A Graph Neural Network-Based Framework for Quantum Circuit Output Prediction

QaML is a Python library that combines quantum computing and machine learning. It uses graph neural networks (GNNs) to predict the expected output values of quantum circuits under both noisy and noiseless conditions, providing new ideas for quantum circuit performance evaluation and variational quantum eigensolver (VQE) optimization. The project is maintained by the QUANTUM-AND-ML team, with code hosted on GitHub. The related paper, "Output prediction of quantum circuits based on graph neural networks", was published in the Frontiers of Physics journal.

Quantum computing, as an important direction of next-generation computing technology, has made significant progress in recent years. However, quantum circuit simulation and prediction face two major challenges: First, the increase in the number of qubits leads to an exponential growth in the dimension of the state space, making it difficult for classical computers to accurately simulate large-scale circuits. Second, real quantum devices have noise interference, leading to deviations between actual outputs and theoretical predictions.

Traditional simulation methods (full wavefunction simulation, tensor networks) see a sharp rise in computational cost as circuit scale expands. After machine learning methods were introduced into the quantum computing field, the QaML project innovatively uses GNNs to process quantum circuits—since quantum circuits naturally have a graph structure (quantum gates as nodes, qubit connections as edges), GNNs are ideal tools.

Graph Representation of Quantum Circuits

Convert quantum circuits into graph structures: nodes represent quantum gate operations, edges represent qubit connections, and node feature vectors include gate type, parameters, and noise information—this preserves the topological structure while facilitating GNN processing.

Noise Modeling

Noise information is introduced into node feature design, enabling the model to learn the impact of noise on outputs and adapt to the needs of real quantum devices.

Two Prediction Schemes

• Indirect comparison scheme: Predict the ground state energies of two parameterized quantum circuits (PQCs) separately and then compare them—intuitive but prone to error accumulation.
• Direct comparison scheme: A core innovation that merges two circuits into a single graph, with node features including noise information, to directly predict relative performance. Experiments show that this scheme improves prediction accuracy by an average of 36.2% compared to the indirect scheme.

QaML provides a complete Python implementation, with main modules including:

• Dataset generation: Dataset.py (large-scale dataset generation and storage), CNN_generate_datas.py (random quantum circuit data), GNN_generate_datas.py (hydrogen molecule ground state energy calculation data);
• Model architecture: CNNs.py (convolutional neural networks), GNNs.py (graph neural networks), circuit_to_graph.py (circuit-to-graph class);
• Computation modules: expectation_and_ground_state_energy_calculation.py (expected value and ground state energy calculation), simplification.py (circuit simplification rules);
• Training and testing: main.py (dataset splitting, model training and testing workflow).

Single-Qubit Expected Value Prediction

With or without noise, GNNs can accurately predict the expected output values of quantum circuits.

Comparison with CNNs

Due to the graph structure characteristics of quantum circuits, GNNs perform better than convolutional neural networks (CNNs).

Scalability Analysis

The change in model performance as the number of qubits increases is discussed, and the potential for practical applications is evaluated.

Performance Comparison in VQE Scenarios

In hydrogen molecule ground state energy prediction, the direct comparison scheme improves accuracy by an average of 36.2% compared to the indirect scheme, verifying the effectiveness of the method.

The results of QaML can be applied to:

• Quantum circuit optimization: Quickly predict circuit performance and efficiently search for optimal designs;
• Noise mitigation strategy evaluation: Predict outputs under different noise conditions and evaluate the effectiveness of mitigation strategies;
• Variational quantum algorithm acceleration: Reduce the computational overhead of optimization processes for algorithms like VQE;
• Quantum-classical hybrid computing: Provide tools for hybrid frameworks to assist in quantum computing optimization and simulation.

By representing quantum circuits as graph structures and encoding noise information, QaML has successfully developed a GNN framework that accurately predicts quantum circuit outputs. The direct comparison scheme is a core innovation—by predicting the relative performance of circuits, it significantly improves accuracy and provides inspiration for similar problems.

As quantum computing develops, the demand for efficient simulation tools is urgent, and QaML provides an exploration direction for quantum-classical hybrid computing. In the future, we look forward to more interdisciplinary research to promote the joint progress of quantum computing and machine learning.