/VQE-Harmonic-Oscillator

This is a simple proof of concept of using Qiskit's VQE and Wolfram Mathematica to find the ground eigenvalue of a Quantum Harmoinc oscillator

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VQE-Harmonic-Oscillator

This is a simple proof of concept of using Qiskit's VQE to find the ground eigenvalue of a Quantum Harmoinc Oscillator and small cubic and quartic perturbations of an Harmonic Oscillator. I have done runs using the Aer simulator with and without simulated noise and on a real device (IBMQ_Manila).

Note that we utilize a discrete version of the Hamiltonian, which means eigenvalues won't agree for the entire spectrum. Fortunately they do agree at the ground state.

I also included a powerpount presentation and handouts for this project.

DEPRECATED Steps (Old files in Archive folder)

The previous method required the use of Wolfram Mathematica to crete and decompose the HAmiltionian into Pauli matrix sums.

  1. Load the Mathematica notebook H_QHO to create the Hamiltonian.
  2. Load the Mathematica notebook Pauli_decomp to decompose the Hamiltonian to a Pauli tensor product.
  3. Load the output file paulis_QHO into Qiskit via the jupyter notebook VQE_QHO.

Files are located in the proper folders inside Archive with an example Hamiltonian and its decomposition.