I will describe the application of two classic notions from linear systems theory to the quantum domain: (i) model realization, the notion of constructing a dynamical model from input-output data only, and (ii) model reduction, the notion of developing compressed descriptions of system dynamics.
First I will detail how model realization methods can be used to develop a technique for estimating parameters in quantum Hamiltonians directly from input-output data (arXiv:1401.5780). This method is particularly advantageous in scenarios with restricted system access and nontrivial prior information.
In the second part of the talk I will present methods that allow for construction of reduced order models for quantum dynamics based on identifying invariant subspaces of Hamiltonians (arXiv:1406.7069). These methods reduce the burden of simulating some models of quantum many-body dynamics.
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