To make a low-resolution logo high resolution in Photoshop you need to increase the size and the resolution in the Image Size window. Go to Image then Image Size and the dialogue box will appear. make the size of the longest end between 3000 to 5000 ppi and the resolution 300 ppi. If the logo is still pixelated, turn it into a smart object then, apply a smart filter, apply a Gaussian blur and then use a curves layer to adjust the image until the pixelated sections are straight. Merge the layers and save as a vector.