Variational Quantum Eigensolver (VQE) - RPIQuantumComputing/QuantumCircuits GitHub Wiki

Description

The Variational Quantum Eigensolver, usually abbreviated as VQE, is a hybrid algorithm which uses both quantum and classical computing to, in the general case, minimize some objective function which can be expressed as a quantum observable. An observable here just refers to some physical property of the system. Most commonly, this observable is the Hamiltonian; an operator which provides the total energy of some system. For the sake of this introduction, we will be assuming calculation of the ground state. But before going any further, let us explore the three main components in a VQE.

Main Components

Cost Function

The cost function is the responsible for producing the expected value of the Hamiltonian. Each time the ansatz has its parameters adjusted, the cost function is responsible for reevaluating the expected Hamiltonian.

Classical Optimizer

The classical optimizer is responsible for reading this evaluation and readjusting the parameters of the quantum circuit which is the ansatz to get closer to the actual ground state.

Ansatz

The Ansatz is the parameterized quantum circuit which serves as a sort of guess as to the ground state of the system.

The system starts with the ansatz, serving as an initial guess as to what the ground state of the system is. Using this ansatz, the cost function is then used to calculate the expected Hamiltonian. Equipped with the expected Hamiltonian, the classical optimizer then recalculates the parameters for the ansatz. This process is continuously repeated until a good approximation of the ground state can be found.

Uses

Implementation

Appendix