# Harnessing Quantum Power: The Variational Quantum Eigensolver

## School Name

South Carolina Governor's School for Science and Mathematics

## Grade Level

12th Grade

## Presentation Topic

Computer Science

## Presentation Type

Mentored

## Abstract

Despite the raw computational power of classical computers, some problems require an exponential amount of computation time. Quantum algorithms aim to solve these problems by leveraging the unique properties of quantum mechanics. One of these algorithms is the Variational Quantum Eigensolver, which finds the minimum eigenvalue of a Hermitian matrix. Through Microsoft’s Quantum API, Qiskit, we implemented the VQE, completed a resource estimation and use several of IBM’s quantum simulations/computers. To recreate the algorithm, we referenced Microsoft’s Qiskit textbook and academic papers for potential applications. For finding the ground state energy of a molecule, we first mapped the Hamiltonian matrix to quantum gates. In quantum subroutine, we initialized qubits, then using the compatible Hamiltonian, prepared an ansatz. After measuring the qubits, we computed necessary values in classical post-processing. Using these values, we updated the ansatz parameters. By iteratively improving the quantum parameters, we optimize the path to the solution. We ran our version of the VQE on three IBM resources. We were unable to use a quantum computer because only 7 qubits are available for public use, whereas our code needed 8 qubits. On the statevector simulator, we found the ground state energy of Lithium Hydride with an average margin of error of 0.00041 Hartree. On IBM’s noisy Qasm simulator, the run time significantly lengthened. When noise is introduced, quantum algorithms become less robust. The NISQ era of hardware leaves software developmers with quantum noise/error. As hardware improves, there could be applications in chemical engineering, material science and portfolio optimization.

## Recommended Citation

Cadena, Caroline, "Harnessing Quantum Power: The Variational Quantum Eigensolver" (2023). *South Carolina Junior Academy of Science*. 29.

https://scholarexchange.furman.edu/scjas/2023/all/29

## Location

ECL 340

## Start Date

3-25-2023 9:45 AM

## Presentation Format

Oral Only

## Group Project

No

Harnessing Quantum Power: The Variational Quantum Eigensolver

ECL 340

Despite the raw computational power of classical computers, some problems require an exponential amount of computation time. Quantum algorithms aim to solve these problems by leveraging the unique properties of quantum mechanics. One of these algorithms is the Variational Quantum Eigensolver, which finds the minimum eigenvalue of a Hermitian matrix. Through Microsoft’s Quantum API, Qiskit, we implemented the VQE, completed a resource estimation and use several of IBM’s quantum simulations/computers. To recreate the algorithm, we referenced Microsoft’s Qiskit textbook and academic papers for potential applications. For finding the ground state energy of a molecule, we first mapped the Hamiltonian matrix to quantum gates. In quantum subroutine, we initialized qubits, then using the compatible Hamiltonian, prepared an ansatz. After measuring the qubits, we computed necessary values in classical post-processing. Using these values, we updated the ansatz parameters. By iteratively improving the quantum parameters, we optimize the path to the solution. We ran our version of the VQE on three IBM resources. We were unable to use a quantum computer because only 7 qubits are available for public use, whereas our code needed 8 qubits. On the statevector simulator, we found the ground state energy of Lithium Hydride with an average margin of error of 0.00041 Hartree. On IBM’s noisy Qasm simulator, the run time significantly lengthened. When noise is introduced, quantum algorithms become less robust. The NISQ era of hardware leaves software developmers with quantum noise/error. As hardware improves, there could be applications in chemical engineering, material science and portfolio optimization.