Quantum error mitigation via machine learning

Abstract

Quantum computers have attracted attention to have overwhelming performance compared to classical computers through exponential speed up. However, existing quantum computers have not yet shown such performance, and also quantum computers have not shown satisfactory accuracy due to large errors. Research on quantum error correction has been conducted for decades, but existing quantum computers have too large errors to apply such quantum error correction methods. Therefore, studies on various quantum error mitigation methods have been recently conducted.

This dissertation focuses on quantum error mitigation via machine learning. And it is made up of two parts, analyzing and predicting quantum states and mitigating errors in quantum circuits. First, to analyze and predict the quantum state, the quantum states of the Rydberg atom are measured by simulating with dephasing error and experimenting on the real environment. After that, we propose a method to predict quantum states through artificial neural networks and Long Short-Term Memory (LSTM). With the proposed method, we measure the probability of each computational basis of the quantum state, and base on the measurement outcome, we predict the measurement probability for the future state.

By applying this prediction method to quantum circuits, we also propose the quantum error mitigation method on quantum circuits via machine learning. The error of the IBM quantum cloud platform is mitigated through artificial neural networks and convolutional neural networks. The measurement probability is obtained by simulating the quantum circuit using the error model of the IBM quantum cloud and by actually experimenting on the IBM quantum cloud platform. Measurement probability for each computational basis is obtained, and errors of measurement probability are mitigated according to the gate configuration. Moreover, we compare the mitigation efficiency according to the input permutation and the degree of quantum entanglement.