MPS-GDS
Gradient Descent Optimization of MPS for Ground State Finding
Report submission for the Quantum Many Body Physics course of the Quantum Science and Technology master’s degree at the Technische Universität München.
- Project repository.
Abstract:
In this paper I will explore the implementation of the gradient descent method (GDS) to find the ground state of the Ising Hamiltonian employing Matrix Product States (MPS) algorithms. After a brief theoretical introduction, I explore the parameter regimes that best suit the algorithm, including the optimization of the ansatz state, learning rate, and Hamiltonian parameters. The comparison of GDS against other well-known algorithms for ground state preparation, such as TEBD and DMRG, showcases the deficiencies of the algorithm. I then finalize the work with a discussion of possible improvements as well as comments on its implementation.