Contents
What are the inputs to The VQE algorithm?
The inputs to the VQE algorithm are a molecular Hamiltonian and a parametrized circuit preparing the quantum state of the molecule. Within VQE, the cost function is defined as the expectation value of the Hamiltonian computed in the trial state.
When to use variational quantum Eigensolver ( VQE )?
The Variational-Quantum-Eigensolver (VQE) [1, 2] is a quantum/classical hybrid algorithm that can be used to find eigenvalues of a (often large) matrix (H).
Which is the object for holding optimization results from VQE?
Object for holding optimization results from VQE. VQE is an object that encapsulates the VQE algorithm (functional minimization).
Which is the best classical optimizer for VQE?
When utilizing VQE in either a noisy simulator or on real hardware, SPSA is recommended as the classical optimizer. When noise is not present in the cost function evaluation (such as when using VQE with a statevector simulator), a wide variety of classical optimizers may be useful.
How is the cost function defined in VQE?
The next step is to define the cost function to compute the expectation value of the molecular Hamiltonian in the trial state prepared by the circuit. We do this using the ExpvalCost class, which is tailored for VQE optimization.
How is the action represented in a VQE circuit?
VQE does so through the use of a parameterized circuit with a fixed form. Such a circuit is often called a variational form, and its action may be represented by the linear transformation U (θ) U ( θ).
How is VQE an application of the Ritz variational principle?
It is an application of the Ritz variational principle, where a quantum computer is trained to prepare the ground state of a given molecule. The inputs to the VQE algorithm are a molecular Hamiltonian and a parametrized circuit preparing the quantum state of the molecule.
How do you simulate a molecule in VQE?
The first step is to specify the molecule we want to simulate. This is done by providing a list with the symbols of the constituent atoms and a one-dimensional array with the corresponding nuclear coordinates in atomic units. The molecular structure can also be imported from an external file using the read_structure () function.