Theory Seminar: Quantum algorithms for powering stable Hermitian matrices

Guillermo González (MPQ)
In the talk I will present our recent paper arXiv:2103.08329.

Guillermo González (MPQ)
Group Seminar via Zoom
Wed 21. April 2021, 11:30 am (MEZ)

Abstract:

In the talk I will present our recent paper arXiv:2103.08329. In the paper we investigate the possibility of speeding up matrix powering of sparse stable Hermitian matrices on a quantum computer. We present two quantum algorithms that can achieve speedup over the classical matrix powering algorithms -- (i) and adaptation of quantum-walk based fast forwarding algorithm (ii) an algorithm based on Hamiltonian simulation. Furthermore, by mapping the N-bit parity determination problem to a matrix powering problem, we provide no-go theorems that limit the quantum speedups achievable in powering non-Hermitian matrices.

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