Variational Quantum Eigensolver
Find the expectation value of the Hamiltonian Z ⊗ Z, with respect to an arbitrarily constructed trial state using parametrize quantum circuit in Qiskit. Where Z = z-component of Pauli vector.
The Variational quantum eigensolver consists a total of three subroutines:
- Trial State Preparation: This can be done by choosing an arbitrary quantum gate sequence (ansatz), depending on some parameters i.e. angles.
- Finding the Energy: After preparing the initial state one need to find the expectation value of Hamiltonian (i.e. energy) on the basis of the prepared trial state.
- Minimize the Energy: This step can be efficiently done by using a completely classical process, and by choosing an optimization method from the scipy.optimize documentation of Python.
This project can be completed by using only first two subroutines of VQE process. Hence your task will be to:
- Construct a trial wave function using an arbitrary parametrized quantum circuit i.e. ansatz based on single qubit gates and two qubit rotating gates.
- Find the expectation value of Z ⊗ Z, in the basis of the trial wave function i.e. Expectation Value = ⟨trial state|Z ⊗ Z|trial state⟩
The Trial state can be obtained by using the Statevector Simulator after running the parametrized quantum circuit mentioned in the first step i project elaboartion.
- Michał Stęchły's blogpost: https://www.mustythoughts.com/variational-quantum-eigensolver-explained
- Frank Zickert's Article: https://towardsdatascience.com/the-variational-quantum-eigensolver-explained-adcbc9659c3a
- JavaFXpert's article: https://medium.com/qiskit/the-variational-quantum-eigensolver-43f7718c2747
- Prof. K.L. Sebastian's lecture on Variational Methods(the backbone of VQE): https://www.youtube.com/watch?v=T-wXwgS7MuI