Quantum state tomography of n-qubit quantum mechanical system.

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Name of the Speaker: Mr. Siva Shanmugam P (EE17S024)
Guide: Dr. Sheetal Kalyani
Venue: ESB-244 (Seminar Hall)
Date/Time: 3rd February 2023 (Friday), 10:00 AM

This talk presents two methods proposed for estimating the state of n-qubit quantum systems as part of my M.S. work (More focus on the second method).

In order to motivate the talk, a simple quantum system namely "qubit" will be discussed. This will be done by explaining the polarization of light (Electromagnetic radiation) which realizes a qubit just as an on-off switch realizes a classical bit. The state of polarization of light and the measurements of it will be discussed which will then lead to formally stating the problem considered in this work.

At the end of any quantum operation carried on a quantum computer, there is a need to estimate the state of quantum systems. Although these computations are "quantum", the estimation of the quantum states (represented by a complex matrix) can be performed using classical computers from their measurements. To this end, we propose two methods. The first method incorporates prior knowledge about the state and estimates the quantum state by inverting the linear relation between the state and the measurements obtained. This method provides a closed form expression for the estimate because of which the estimation is performed much faster than any iterative methods. Two caveats of this method are as follows. 1) It requires an informationally complete set of measurements which is exponential in the size of the system (n). 2) The estimate may not be positive semidefinite which is a property of the quantum state.

To overcome the above said caveats, in the second work, a neural network for quantum estimation is designed based on a popular iterative algorithm named Singular Value Thresholding (SVT). The proposed network estimates low-rank quantum states from fewer measurements than that is required for an informationally complete set. Since the network is tailored to quantum state tomography, the estimate is always a valid quantum state. The proposed network is computationally more efficient than SVT in the sense that a 3-layered network (equivalent of 3 SVT iterations) outperforms SVT (in terms of fidelity) which converges in 1700 iterations.