As we can see from the loaded dataset, it's a 64-dimensional dataset. Now let's use scikit-learn's PCA() function to find the two dominant principal components of this dataset and project the dataset along these two dimensions, followed by scatter-plotting the projected data with Matplotlib and with each data point representing an image (a digit), with the digits label represented by a unique color, using the following code block:

pca_digits=PCA(2)
digits.data_proj = pca_digits.fit_transform(digits.data) 
print(np.sum(pca_digits.explained_variance_ratio_))
# 0.28509364823696987
plt.figure(figsize=(15,10))
plt.scatter(digits.data_proj[:, 0], digits.data_proj[:, 1], lw=0.25, c=digits.target, edgecolor='k', s=100, cmap=plt.cm.get_cmap('cubehelix', 10))
plt.xlabel('PC1', size=20), plt.ylabel('PC2', size=20), plt.title('2D Projection of handwritten digits with PCA', size=25)
plt.colorbar(ticks=range(10), label='digit value')
plt.clim(-0.5, 9.5)

The following screenshot shows the output. As can be seen, the digits are somewhat separated (although there is some overlap) even in the 2D projection along the PCs, with same digit values appearing nearby in clusters: