Output Prediction of Quantum Circuits based on Graph Neural Networks

TL;DR

Simulations 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.

Abstract

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.

Figures (14)

• Figure 1: The framework for expectation values prediction. a) Generate random quantum circuits. b) Transform the random quantum circuits into graph structures. c) Incorporate noise information into the graph nodes of the quantum circuits, train GNNs, and predict the expectation values of quantum circuits.
• Figure 2: Random circuits generation and circuits optimization.
• Figure 3: Node feature vector.
• Figure 4: Overview of the GNNs for the expectation value prediction.
• Figure 5: Randomly generated single layer parameterized quantum circuit (PQC) with the quantum gates enclosed in dashed boxes representing those not selected.