Quantum devices keep growing in size and complexity, but at the same time extracting precise information about wave-functions and Hamiltonians remains fundamentally limited by qunatum mechanics: single measurement, weak or strong, can give us only limited amount of information about these general objects living in complex Hilbert spaces. I am very interested in developing methods that can extract maximum amount of device information from as little measurements as possible and tailor them to exisitng experiments.
Parameter Estimation for Quantum Devices
In experiments with quantum devices we do not in most cases have access to measurements for reconstruction of the whole wavefunction.
Using probability theory, machine learning or combination of both we can still reconstruct the key parameters for the system dynamics. We implemented these ideas for quantum dots: Phys. Rev. A 96, 052104 (2017) and arXiv:1711.05238 as well as for superconducting qubits: Phys. Rev A 94, 042334 (2016).
Currently I am interested in how to expand these methods to scales that cannot be simulated on classical computers.
Verification of large-scale quantum simulators
Contemporary large-scale quantum experiments are facing the following challenge: On one hand we build devices that no classical computer can simulate, on the other we would like to check that quantum device does what we want it to. In arXiv: 2103.01240 we propose a concrete strategy to resolve this contradiction for large-scale quantum simulators based on ultracold atoms. Specifically, we show how to scale Hamiltonian learning on the subsystems on the device to the arbitrary device size in quasi-1D.