To make stereoscopic spherical panoramas, you need PT3D
PT3D helps PTGui align and stitch stereo pair photos into stereo spheres.
It gives excellent results with typical 2D shooting patterns, and can handle
large numbers of views as well.
PT3D automates alignment and warping, but you will still need some skill
at using PTGui masks to hide small stitching errors.
PT3D is licensed per seat, meaning one user name on one computer. You
can buy a license for one or more seats, and get activation codes by email.
New users can get a free 30-day evaluation license.
The current release is version 1.4.3 (12 April 2018) -- improved stabilization