Articles

# Quantum Algorithms: Quantum Approximate Optimization Algorithm (QAOA)

25
March
,
2022

Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum/classical algorithm that helps solve combinatorial optimization problems. As these problems grow larger, solving them using classical computers becomes impractical. QAOA is useful for the worst cases - those most difficult to construct - of NP complete problems.

Some applications of QAOA include infrastructure optimization - designing networks of highways, utility poles, air-traffic, and shipping routes - and financial optimization - minimizing risk and maximizing profits for a given portfolio.

QAOA is a special case of the VQE algorithm, where we’re finding a state that satisfies the optimization problem, not specifically the ground state. The algorithm is a parameterization of an ansatz, or initial state. It consists of an initialization, defining all possible solutions; a cost function, specifying the constraints; and a mixer function, allowing the whole space of solutions to be explored. To learn more about how QAOA works, read more here or here.

Users of the Classiq platform have two flavors of QAOA to choose from: 1) the original QAOA and 2) the Quantum Alternating Optimization Ansatz.

1. Original QAOA (Quantum Approximate Optimization Algorithm). Here the constraints are expressed as penalty terms in the objective function. The optimization process will discourage solutions that don’t obey the constraints. The search space spans the entire Hilbert space and the algorithm mixes all the possible solutions.
2. New QAOA (Quantum Alternating Optimization Ansatz). This algorithm explicitly constrains the search space in accordance with the problem constraints. The constraints are embedded in the initialization and mixer layers.

In a recent presentation, Classiq showed how quantum computing can help with optimization problems. See it here

Want to see how your business could implement QAOA for solving optimization problems? Schedule a demo today!

Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum/classical algorithm that helps solve combinatorial optimization problems. As these problems grow larger, solving them using classical computers becomes impractical. QAOA is useful for the worst cases - those most difficult to construct - of NP complete problems.

Some applications of QAOA include infrastructure optimization - designing networks of highways, utility poles, air-traffic, and shipping routes - and financial optimization - minimizing risk and maximizing profits for a given portfolio.

QAOA is a special case of the VQE algorithm, where we’re finding a state that satisfies the optimization problem, not specifically the ground state. The algorithm is a parameterization of an ansatz, or initial state. It consists of an initialization, defining all possible solutions; a cost function, specifying the constraints; and a mixer function, allowing the whole space of solutions to be explored. To learn more about how QAOA works, read more here or here.

Users of the Classiq platform have two flavors of QAOA to choose from: 1) the original QAOA and 2) the Quantum Alternating Optimization Ansatz.

1. Original QAOA (Quantum Approximate Optimization Algorithm). Here the constraints are expressed as penalty terms in the objective function. The optimization process will discourage solutions that don’t obey the constraints. The search space spans the entire Hilbert space and the algorithm mixes all the possible solutions.
2. New QAOA (Quantum Alternating Optimization Ansatz). This algorithm explicitly constrains the search space in accordance with the problem constraints. The constraints are embedded in the initialization and mixer layers.

In a recent presentation, Classiq showed how quantum computing can help with optimization problems. See it here

Want to see how your business could implement QAOA for solving optimization problems? Schedule a demo today!

## 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.