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GGD/GEAR/Quantum Topology Seminar: The k-local Cohomology Problem and the Complexity of Supersymmetric Systems

Event Type
wifi event
Jan 27, 2022   12:00 - 1:00 pm   Central
Marcos Crichigno
Eric Samperton

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.

Meeting ID: 881 6087 3184

Password: PSL27

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