The earliest attempt to study electronic structure of atoms is nearly as old as the discovery of subatomic particles itself. Several theories to approximate molecular orbitals have been developed, nevertheless determining precise electronic structure of large molecules is one of the most challenging problems, so much so that we are looking forward to quantum computers to solve it. 

Tensor networks are efficient tools to study quantum many body physics and chemistry as one could i) represent states of many body systems in the form of n-dimensional tensors as nodes ii) Keep track of correlations between different states as edges in a graph. However computational complexity of a general tensor network can be huge, where contraction algorithms have an overall complexity that is a multiple of the individual complexity of a single tensor. As a result, scaling has a drastic impact on computational resources and it is desirable to have an orthogonal basis of electronic structure to get diagonal/sparse tensors. 

In our thesis the primary goal is to find an orthogonal and complete basis set which can solve the Schrodinger equation of multi-electron systems. We have described unitary circuit methodology discovered by Steven White to generate an orthogonal basis just by using a sequence of linear transformations. Later we will go into detailed implementation of orthogonal Gausslet basis and apply it to trapped ion and quantum dot systems. The scope of our work can be further extended to finding computationally efficient algorithms to calculate expectation value (and hence energy corresponding to a given electronic state).