Plans for the week of March 2-6

Dear all, welcome back to FYS5419/9419.? Here are our plans for the present week.

Plans for the week of March 2-6

Reminder on basics of the VQE method and how to perform measurements for the simpler one- and two-qubit Hamiltonians

Simulating efficiently the two-qubit Hamiltonians on quantum computers with the VQE method and gradient descent to optimize the state function ansatz

Introducing the Lipkin model and how to program it with the VQE

Work on project 1 during lab/exercise sessions

Readings and notebooks

For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11 and 3.1-3.4 of Hundt's book?Quantum Computing for Programmers, contain most of the relevant information.

The VQE algorithm is discussed in Hundt's section 6.11, note that the solution of the two-qubit system is outdated, measuring on one qubit only is not the present standard, see additional notes below and the jupyter-notebooks

See also the VQE review article by Tilly et al.

Jupyter-notebook on VQE and single-qubit problem from last week at?https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week6/ipynb/single_qubit_vqe_modified.ipynb

Jupyter-notebook on VQE and two-qubit problem at?https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week6/ipynb/two_qubit_vqe_modified.ipynb

More material

Notes on why we measure on all qubits and not on one as in Hundt's chapter 6.11, see additional pdf file at?https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week7/pdf/measurenotes.pdf

Jupyter-notebook on VQE for the Lipkin model at?https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week7/ipynb/lipkinvqe.ipynb

During the lab session we will keep working on the project. For the lecture, the main focus will be on implementing the VQE with measurements for two qubits and how to set up the VQE for the Lipkin model. The above jupyter-notebooks can hopefully be of some help.

Best wishes,

Carl Fredrik and Morten