Mafalda Ramôa

This repository contains the code I developed for my thesis, submitted for the degree of Master of Science in the Engineering Physics course at University of Minho (Physics of Information branch).

You can access the thesis on arXiv.

Implementation of Adapt VQE ([1][2]), using the CIRQ simulator for the evaluation of both the energy and the gradient, and OpenFermion, PySCF and their plug-in for the chemistry part. Includes:

• A noise free, matrix algebra based version of the algorithm.
• The possibility of removing terms or growing the ansatz conservatively (multiple optimization attempts per iteration).
• Multiple pool options (the ones used in Qubit Adapt [1] and Fermionic Adapt [2], and others).
• Functions to estimate the required numer of CNOTs.
• Functions to examine the Slater determinants in the state.
• Plots for the evolution of the energy, comparing runs, etc.

Simpler, function-based version of Adapt VQE using the CIRQ simulator for the evaluation of both the energy and the gradient, and OpenFermion, PySCF and their plug-in for the chemistry part. Includes:

• A noise free, matrix algebra based version of the algorithm.
• Multiple pool options (the ones used in Fermionic Adapt and Qubit Adapt, and others).
• Energy calculation functions, with and without sampling noise, and tests to check their performance, as well as the impact of trotterization and sampling noise on the energy evaluation.
• Gradient calculation functions, with and without sampling noise, and tests to check their performance, as well as the impact of the number of shots on the precision.
• Basic energy plots.

Exploring simple functionalities of Openfermion along with CIRQ.

Implementation of VQE with the unitary coupled cluster singles and doubles ansatz, using the CIRQ simulator for the energy expectation, and Openfermion, PySCF and their plug-in for the chemistry part. Includes:

• A noise free, matrix algebra based version of the algorithm.
• Analysis of the number of operators in the UCCSD ansatz.
• Tests on the expectation estimation, with and without trotterization, and with or without sampling noise.
• Multiple methods for trotterizing operators, and tests on their application to Hamiltonians and the UCCSD operator.
• Analysis of the effect of the starting point, trotterization, sampling noise, and choice of optimizer.

Implementation of the original VQE algorithm [3] using the CIRQ simulator for the energy expectation. The algorithm is applied to HeH+, using the Hamiltonian from that paper, and the same ansatz (spanning the whole 2-qubit Hilbert space). Includes:

• A noise free, matrix algebra based version of the algorithm.
• Functions to create a circuit to prepare an arbitrary two qubit state from its parameterization, based on Schmidt decomposition.
• Plot comparing the median and average of the energy.
• Plot with the median of the energy, with interquartile ranges as error bars.
• Tests on the energy expectation and state preparation.

Attempts to minimize the hyperparameters for the Nelder Mead optimization: tolerance (fatol, xatol) and the initial simplex size (through a single parameter delta). Current values were result of using a cost function penalizing overlaps with the ground state under 90%, and the number of failed attempts until converging.

Implementation of the Adapt VQE algorithm, using Qiskit for evaluation of the energy, and OpenFermion, PySCF and their plug-in for the chemistry part.

• A noise free, matrix algebra based version of the algorithm..
• Noise models for thermal relaxation, SPAM noise,...
• Qubit Adapt [1] and Fermionic Adapt [2] pools.
• Plot for the evolution of the energy
• Trotterization of OpenFermion's QubitOperator into Qiskit circuits.
• Transformation of OpenFermion's Hamiltonian into Qiskit Aqua observables.

Implementation of VQE with the unitary coupled cluster singles and doubles ansatz, using Qiskit for the energy expectation, and PySCF and its Qiskit Driver for the chemistry part. Includes:

• A noise free, matrix algebra based version of the algorithm..
• Noise models for thermal relaxation, SPAM noise,...
• Numerical results.
• A plot of the evolution of the energy along the optimization.

Implementation of the original VQE algorithm [3] using Qiskit for the energy expectation. The algorithm is applied to HeH+, using the Hamiltonian from that paper, and the same ansatz (spanning the whole 2-qubit Hilbert space). Includes:

• A noise free, matrix algebra based version of the algorithm.
• Plot of the evolution of the energy and overlap with the ground state along the optimization.

[1] Ho Lun Tang, V. O. Shkolnikov, George S. Barron, Harper R. Grimsley, Nicholas J. Mayhall, Edwin Barnes, and Sophia E. Economou. qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor. Preprint arXiv arXiv:1911.10205 [quant-ph].

[2] Harper R. Grimsley, Sophia E. Economou, Edwin Barnes, and Nicholas J. Mayhall. An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications, 10(1), 3007 (2019).

[3] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Al ́an Aspuru-Guzik, and Jeremy L. O’Brien. A variational eigenvalue solver on a photonic quantum processor. Nature Communications 5 (1), 4213 (2014).