量子神經網路求解微分方程

Abstract

近年來，基於變分量子電路（VQC）的機器學習算法已在函數逼近，分類和深度強化學習中獲得成功。 在這項工作中，我們將VQC的功能擴展到了求解常微分方程（ODE）和偏微分方程（PDE）的領域。 在這項工作中，我們使用一種量子資訊編碼方法將古典資料準備成量子態，以供量子電路學習微分方程解。 所提出的框架可以在許多近期有噪聲的中尺度量子（NISQ）設備中實現，因此對於量子計算機在科學計算中的應用具有價值。

Recently, machine learning algorithms based on variational quantum circuits (VQC) have been successful in function approximation, classification and deep reinforcement learning. In this work, we extend the capability of VQC to the domain of solving ordinary differential equations (ODE) and partial differential equations (PDE). In this work, we use a quantum information encoding method to prepare classical values into quantum states for a quantum circuit to learn the differential equation solutions. The proposed framework can be implemented in many near-term noisy intermediate scale quantum (NISQ) devices and therefore is invaluable for the application of quantum computers in scientific computing.