I will discuss various aspects on the interplay of supersymmetry, quantum computation, and computational topology. After introducing some basic elements of supersymmetric quantum mechanics and elements of quantum complexity theory, I will show that the determining the computational complexity of various problems in computational topology/cohomology amounts to determining the Hamiltonian complexity of supersymmetric systems. In particular, studying the k-local Hamiltonian problem for supersymmetric systems will lead us to define the problem “k-local cohomology” and I will show that its complexity lies somewhere between QMA_1 and QMA. This reveals that many problems in computational topology/cohomology are intrinsically quantum mechanical. No prior knowledge of supersymmetry or cohomology will be assumed.
https://illinois.zoom.us/j/88160873184?pwd=azZzdkFLUjhRWlY5TnA0TWFOdWZ1UT09
Meeting ID: 881 6087 3184
Password: PSL27
