An implementation of quantum convolutional neural network with MindQuantum. Huawei, classifying MNIST dataset

Overview

关于实现的一点说明


文件说明

  • tools.py 这里面主要有两个函数:

    • resize(a, lenb)

    这其实是我找同学写的一个小算法hhh。给出一个$28\times 28$的方阵a,返回一个$lenb\times lenb$的方阵。因为懒得装openCV,于是手动写了一个把图像降低分辨率的操作,原理是根据几何关系计算新的像素值。总之可以把$28\times28$的MNIST原始数据改成$16\times 16$的,这就可以用8个比特encode了。写的可能比较丑陋,但毕竟只是初始化数据用的,所以能用一次性就行了。

    • controlled_gate(circuit, gate, tqubit, cqubits, zero_qubit)

    这其实是因为我发现mindquantum的受控门不支持“空心受控”,于是我就自己写了个。如果$cqubits=[0,-1,2],zero_qubit=1$就表示第一、三量子比特为1时,第二量子比特为0时,才进行运算。就是用负数表示了“空心受控”,然后zero_qubit单独判断了下第0量子比特。(因为它没有符号)

  • test.py: 主程序,里面写注释了。用来训练和预测。

  • MNIST_params.npy:因为我手动写了个实现amplitude encoding的线路,然后该线路也是有参数的,参数是原始数据的各种复合运算。因为我不知道mindquantum支持参数复合运算的操作,于是我就预处理了下数据,把这些参数都算出来了(针对每个样本)。原始数据是$16\times 16=[0,256)$,但encoder中的参数只有$[0,255)$。所以MNIST_params.npy里的数据的规模是$60000\times 255$的。

  • MNIST_train.npy:$60000\times 256$的原始数据

  • MNIST_train_formalized:$60000\times 256$的原始数据,每行都归一化了,方便encoding。

  • weights.npy:我已经训练好的一组ansatz的参数值,在test.py中有用它来预测。

关于原理的一些说明

  • encoder部分是我自己想的hhh,我想了一个可以实现amplitude encoding的线路。复杂度不高。

  • ansatz我选的是https://arxiv.org/pdf/2108.00661.pdf中讲到的convolutional circuit1:

    cc

    pooling层就比较随意的受控RZ和受控RX门

  • 最后就是基于计算基下测量。

  • 然后就是Adam优化啥的都是自带的好东西,一直train就完事了

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