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arXiv:2309.06975 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Predicting Expressibility of Parameterized Quantum Circuits Using Graph Neural Network

Shamminuj Aktar, Andreas Bärtschi, Abdel‐Hameed A. Badawy, Diane Oyen, Stephan Eidenbenz

Published Sep 17, 2023• 6 citations
arXivHTMLPDF

Abstract

Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor influencing their efficacy in solving quantum problems. However, the existing technique for computing expressibility relies on statistically estimating it through classical simulations, which requires many samples. In this work, we propose a novel method based on Graph Neural Networks (GNNs) for predicting the expressibility of PQCs. By leveraging the graph-based representation of PQCs, our GNN-based model captures intricate relationships between circuit parameters and their resulting expressibility. We train the GNN model on a comprehensive dataset of PQCs annotated with their expressibility values. Experimental evaluation on a four thousand random PQC dataset and IBM Qiskit's hardware efficient ansatz sets demonstrates the superior performance of our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06, respectively.

DOI
10.1109/qce57702.2023.10302

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Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor influencing their efficacy in solving quantum problems. However, the existing technique for computing expressibility relies on statistically estimating it through classical simulations, which requires many samples. In this work, we propose a novel method based on Graph Neural Networks (GNNs) for predicting the expressibility of PQCs. By leveraging the graph-based representation of PQCs, our GNN-based model captures intricate relationships between circuit parameters and their resulting expressibility. We train the GNN model on a comprehensive dataset of PQCs annotated with their expressibility values. Experimental evaluation on a four thousand random PQC dataset and IBM Qiskit's hardware efficient ansatz sets demonstrates the superior performance of our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06, respectively.
Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model's predictions with reference circuits from Sim et al. and IBM Qiskit's hardware-efficient ansatz sets to further evaluate our model's performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model's efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.
This article proposes a Graph Neural Network (GNN) approach to estimate nonstabilizerness in quantum circuits, measured by the stabilizer Rényi entropy (SRE). Nonstabilizerness is a fundamental resource for quantum advantage, and efficient SRE estimations are highly beneficial in practical applications. We address the nonstabilizerness estimation problem through three supervised learning formulations starting from easier classification tasks to the more challenging regression task. Experimental results show that the proposed GNN manages to capture meaningful features from the graph-based circuit representation, resulting in robust generalization performances achieved across diverse scenarios. In classification tasks, the GNN is trained on product states and generalizes on circuits evolved under Clifford operations, entangled states, and circuits with higher number of qubits. In the regression task, the GNN significantly improves the SRE estimation on out-of-distribution circuits with higher number of qubits and gate counts compared to previous work, for both unstructured random quantum circuits and structured circuits derived from the transverse-field Ising model. Moreover, the graph representation of quantum circuits naturally integrates hardware-specific information. Simulations on noisy quantum hardware highlight the potential of the proposed GNN to predict the SRE measured on quantum devices.
The output prediction of quantum circuits is a formidably challenging task imperative in developing quantum devices. Motivated by the natural graph representation of quantum circuits, this paper proposes a Graph Neural Networks (GNNs)-based framework to predict the output expectation values of quantum circuits under noisy and noiseless conditions and compare the performance of different parameterized quantum circuits (PQCs). We construct datasets under noisy and noiseless conditions using a non-parameterized quantum gate set to predict circuit expectation values. The node feature vectors for GNNs are specifically designed to include noise information. In our simulations, we compare the prediction performance of GNNs in both noisy and noiseless conditions against Convolutional Neural Networks (CNNs) on the same dataset and their qubit scalability. GNNs demonstrate superior prediction accuracy across diverse conditions. Subsequently, we utilize the parameterized quantum gate set to construct noisy PQCs and compute the ground state energy of hydrogen molecules using the Variational Quantum Eigensolver (VQE). We propose two schemes: the Indirect Comparison scheme, which involves directly predicting the ground state energy and subsequently comparing circuit performances, and the Direct Comparison scheme, which directly predicts the relative performance of the two circuits. Simulation results indicate that the Direct Comparison scheme significantly outperforms the Indirect Comparison scheme by an average of 36.2% on the same dataset, providing a new and effective perspective for using GNNs to predict the overall properties of PQCs, specifically by focusing on their performance differences.
The growing variety of quantum hardware technologies, each with unique peculiarities such as connectivity and native gate sets, creates challenges when selecting the best platform for executing a specific quantum circuit. This selection process usually involves a brute-force approach: compiling the circuit on various devices and evaluating performance based on factors such as circuit depth and gate fidelity. However, this method is computationally expensive and does not scale well as the number of available quantum processors increases. In this work, we propose a Graph Neural Network (GNN)based predictor that automates hardware selection by analyzing the Directed Acyclic Graph (DAG) representation of a quantum circuit. Our study evaluates 498 quantum circuits (up to 27 qubits) from the MQT Bench dataset, compiled using Qiskit on four devices: three superconducting quantum processors (IBM-Kyiv, IBM-Brisbane, IBM-Sherbrooke) and one trappedion processor (IONQ-Forte). Performance is estimated using a metric that integrates circuit depth and gate fidelity, resulting in a dataset where 93 circuits are optimally compiled on the trappedion device, while the remaining circuits prefer superconducting platforms. By exploiting graph-based machine learning, our approach avoids extracting the circuit features for the model evaluation but directly embeds it as a graph, significantly accelerating the optimal target decision-making process and maintaining all the information. Experimental results prove94.4%\mathbf{9 4. 4 \%}94.4%accuracy and an85.5%\mathbf{8 5. 5 \%}85.5%F1 score for the minority class, effectively predicting the best compilation target. The developed code is publicly available on GitHub (https://github.com/antotu/GNN-Model-Quantum-Predictor).
Abstract With the exponentially faster computation for certain problems, quantum computing has garnered significant attention in recent years. Variational quantum algorithms are crucial methods to implement quantum computing, and an appropriate task‐specific quantum circuit ansatz can effectively enhance the quantum advantage of VQAs. However, the vast search space makes it challenging to find the optimal task‐specific ansatz. Expressibility, quantifying the diversity of quantum circuit ansatz states to explore the Hilbert space effectively, can be used to evaluate whether one ansatz is superior to another. In this work, using a transformer model to predict the expressibility of quantum circuit ansatze is proposed. A dataset containing random PQCs generated by the gatewise pipeline, with varying numbers of qubits and gates is constructed. The expressibility of the circuits is calculated using three measures: KL divergence, relative KL divergence, and maximum mean discrepancy. A transformer model is trained on the dataset to capture the intricate relationships between circuit characteristics and expressibility. Four evaluation metrics are employed to assess the performance of the transformer. Numerical results demonstrate that the trained model achieves high performance and robustness across various expressibility measures. This research can enhance the understanding of the expressibility of quantum circuit ansatze and advance quantum architecture search algorithms.
Quantum machine learning (QML) has demonstrated the potential to outperform classical machine learning algorithms in various fields. However, encoding classical data into quantum states, known as quantum data loading, remains a challenge. Existing methods achieve high accuracy in loading single data, but lack efficiency for large-scale data loading tasks. In this work, we propose Neural Circuit Parameter Prediction, a novel method that leverages classical deep neural networks to predict the parameters of parameterized quantum circuits directly from the input data. This approach benefits from the batch inference capability of neural networks and improves the accuracy of quantum data loading. We introduce real-valued parameterization of quantum circuits and a three-phase training strategy to further enhance training efficiency and accuracy. Experimental results on MNIST dataset show that our method achieves a 17.31 % improvement in infidelity score and 108 times faster runtime compared to existing methods. Our approach provides an efficient solution for quantum data loading, enabling the practical deployment of QML algorithms on large-scale datasets.