Quantum-inpired computing is most naturally used for the simulation of quantum systems because it is crucial to find computation friendly parametrizations of their relevant degrees of freedom. Tensor networks provide a practical way to do this. Most prominently, matrix product states (MPS) (a.k.a. tensor trains) are the workhorse DMRG simulations. Much of my research is concerned with extending these methods to allow for local Markovian noise, which can be given in GKSL form.

Tensor network provide powerful and widely used simulation techniques for isolated spin chains. In contrast, for open quantum systems comparably little work has been done. However, any system is coupled to its environment too some extent. Hence, it is very desirable to establish extensions of the known methods to open quantum systems.

Simulation Techniques

Efficient quantum simulations of local Markovian dynamics

Controlled truncation techniques using Lieb-Robinson bounds arXiv:1103.1122

Positivity of matrix product operators (MPOs) is hard to check

A tensor network simulation scheme based on local purifications

Low-rank matrix reconstruction is arguably the first practically relevant computational task that has been solved using quantum-inspired computation (coming from matrix Bernstein inequalities first developed in quantum information theory). We use low-rank matrix reconstruction and tensor completion to develop methods for quantum system characterization, e.g.:

https://arxiv.org/abs/2112.05176 (Gate set tomography as tensor completion)
https://arxiv.org/abs/1701.03135 (Low-rank matrix reconstruction for quantum process tomography)
https://arxiv.org/abs/1803.00572 (... also from average gate fidelities)