You could do some OG lithography (the litho in lithography means "stone") by masking the white or block parts of the QR code and painting on an etchant. I don't know what the best etchants for stone are, but I imagine HF-containing glass etch would do the trick. (Be very, very careful with HF.)

Instead of making the QR code point to something, you could encode the information directly. A short blurb about a person would fit.