Institute: Institute of Mathematical Science (IMSc), Chennai

Principal Investigator: Dr. C M Chandrashekar

Co-Principal Investigator: Prof. S. R. Hassan

Quantum network allows for transformation and transmission of quantum bits (quantum information) between physically separated quantum circuits (or quantum processors) and communicating devices. A quantum network can be obtained by assembling elementary quantum circuits linking outputs of a circuit to input of another circuit. In principle elementary quantum circuit can be channels, quantum operators, quantum effects or state preparation represented with the corresponding linear map. Currently, experimentalists across the world are working with the smart number of quantum circuits and linking between them. With the scaling of quantum processing (circuits) and computing device, the first hurdle that has to be addressed is the errors in operations and defects in network nodes. Errors in operations has been extensively addressed with quantum error correction codes. Physical defects in circuit networks resulting in compromise of transmission of quantum information across the network is an important and practically relevant problem to be addressed. One can draw some similarities with percolation and quantum information flow in defective networks.

We first propose to explore analytically and numerically the percolation of quantum states driven by the tuneable local Hamiltonian. Comparing the critical point (percolation threshold) on different graph structures (connected and broken tales) and various physical system (including frustrated systems) we with work towards the combination of network geometry and efficient Hamiltonian (in algorithmic form) to optimize percolation of quantum state. This with have a large impact on implementing information flow in physical system which are not free from defects. Defects could lead to stowing down or even localization (Anderson localization) of information propagation. The proposed studies with suggest a bounds on the permissible percentage of defects for a given network size/type and geometry.

Non-trivial topologies of quantum network have been shown to be robust against operational errors. With extensive studies of quantum states dynamics in quantum network of non-trivial topologies we with study the bounds on the permissible defects in the network and work towards the efficient and robust architecture for quantum networks. We further propose to explore the channel capacities of the percolating state both on different graph structures with different noisy channels. Work on the channel capacity of percolating quantum information using quantum walks has already been started but this with only be starting point for the more general proposal outlined above which with take a few years of multiple resources and knowledge to make an impact. We will also take into account the experimental groups and systems they work within the country and work towards the architecture for those systems. This will make our proposal directly relevant to the planned mission.

Publications from this project: