  Applications

# Quantum Algorithms: Variational Quantum Eigensolver (VQE)

24
March
,
2022

The Variational Quantum Eigensolver (VQE) is a quantum algorithm that combines quantum and classical techniques to solve optimization problems from industries such as finance, logistics, and chemistry. For instance, VQE is helpful in finding the ground state of a molecule, a property that’s useful for learning more about a chemical molecule and its interactions. Complex financial and logistical combinatorial optimization problems can be solved with VQE, or more specifically with a Quantum Approximate Optimization Algorithm (QAOA), an algorithm from the VQE family. Once we map the problem into mathematical terms, VQE helps us minimize or maximize specific properties, such as the loss function of a portfolio or the distance a delivery truck traverses given a set of dropoff points it needs to visit.

VQE works because of the variational principle, which defines the relationship between the lowest energy of a system and the expectation value of a given state, declaring a lower bound to the expectation value.

The algorithm starts with an initialization, mapping configurations, such as portfolio’s loss functions or a molecule’s electron orbitals, onto qubits, and an ansatz, or an initial parametrized initial of the wave function. After calculating the energy of the guessed state with quantum computing, VQE uses classical optimization methods to minimize this energy, changing the parameters of the ansatz with each iteration. Utilizing a mixer allows the next guess at the state to be chosen from our solution space. After a sufficient number of iterations, parameter changes no longer decrease the energy. In a chemical simulation, for instance, this means that the ground state energy has been approximated.

Because it is a hybrid algorithm that executes relatively short bursts on the quantum computer, VQE is useful even in the NISQ era.

Want to see VQE in action? Check out how Classiq uses VQE to find the ground state of H2 here, or find out how you could use VQE to solve optimization problems here.  The Variational Quantum Eigensolver (VQE) is a quantum algorithm that combines quantum and classical techniques to solve optimization problems from industries such as finance, logistics, and chemistry. For instance, VQE is helpful in finding the ground state of a molecule, a property that’s useful for learning more about a chemical molecule and its interactions. Complex financial and logistical combinatorial optimization problems can be solved with VQE, or more specifically with a Quantum Approximate Optimization Algorithm (QAOA), an algorithm from the VQE family. Once we map the problem into mathematical terms, VQE helps us minimize or maximize specific properties, such as the loss function of a portfolio or the distance a delivery truck traverses given a set of dropoff points it needs to visit.

VQE works because of the variational principle, which defines the relationship between the lowest energy of a system and the expectation value of a given state, declaring a lower bound to the expectation value.

The algorithm starts with an initialization, mapping configurations, such as portfolio’s loss functions or a molecule’s electron orbitals, onto qubits, and an ansatz, or an initial parametrized initial of the wave function. After calculating the energy of the guessed state with quantum computing, VQE uses classical optimization methods to minimize this energy, changing the parameters of the ansatz with each iteration. Utilizing a mixer allows the next guess at the state to be chosen from our solution space. After a sufficient number of iterations, parameter changes no longer decrease the energy. In a chemical simulation, for instance, this means that the ground state energy has been approximated.

Because it is a hybrid algorithm that executes relatively short bursts on the quantum computer, VQE is useful even in the NISQ era.

Want to see VQE in action? Check out how Classiq uses VQE to find the ground state of H2 here, or find out how you could use VQE to solve optimization problems here.

## About "The Qubit Guy's Podcast"

Hosted by The Qubit Guy (Yuval Boger, our Chief Marketing Officer), the podcast hosts thought leaders in quantum computing to discuss business and technical questions that impact the quantum computing ecosystem. Our guests provide interesting insights about quantum computer software and algorithm, quantum computer hardware, key applications for quantum computing, market studies of the quantum industry and more.    