Quantum Approximate Optimization Algorithm (QAOA)

By Anshul Pal Mar 17, 2024 #Quantum Computing
Quantum Approximate Optimization Algorithm (QAOA)Quantum Approximate Optimization Algorithm (QAOA)

The Quantum Approximate Optimization Algorithm (QAOA) is a extensively researched technique designed to tackle combinatorial optimization challenges using NISQ (Noisy Intermediate-Scale Quantum) devices. QAOA’s potential applications span various fields, generating significant interest within the quantum computing research community who closely monitor its performance.

Quantum Approximate Optimization Algorithm (QAOA) Circuits
Quantum Approximate Optimization Algorithm (QAOA) Circuits

Explaining Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA) is a method to find close-to-perfect solutions for problems like finding the best combination of things, such as the shortest route or the most efficient arrangement. Here’s how it works:

  1. First, we define something called a cost Hamiltonian (HC), which basically tells us how good or bad a solution is. The best solution is found by looking at the ground state of this Hamiltonian.
  2. We also define a mixer Hamiltonian (HM), which helps mix things up and explore different possibilities.
  3. Then, we make circuits using these Hamiltonians. One circuit is based on HC, and the other on HM. These circuits are called cost and mixer layers.
  4. We repeat these layers (the cost and mixer layers) a bunch of times (we call this parameter ‘n‘) and create a big circuit.
  5. Next, we start with an initial setup and apply this big circuit to it. We then tweak some numbers in the circuit using classical methods to get the best possible setup.
  6. Finally, we measure the result of the circuit, and what we get are approximate solutions to our optimization problem.

In short, QAOA begins with defining cost and mixer Hamiltonians, then builds circuits using time evolution and layering, and finishes by sampling from the circuit to find an approximate solution. Ready to give it a try?

Applications of QAOA

QAOA has the potential to solve a wide range of optimization problems in various fields, including finance, logistics, and machine learning. Some examples of applications include:

Portfolio Optimization

In finance, QAOA can be used to optimize investment portfolios by finding the best allocation of assets that maximizes returns while minimizing risks.

Traveling Salesman Problem

The Traveling Salesman Problem is a classic optimization problem in which the goal is to find the shortest possible route that visits a set of cities and returns to the starting city. QAOA can be used to find approximate solutions to this problem, which has applications in logistics and route planning.

Machine Learning

QAOA can also be applied to machine learning problems, such as clustering and classification. By formulating these problems as optimization problems, QAOA can help find optimal solutions more efficiently than classical algorithms.

Limitations of QAOA

While QAOA shows promise in solving optimization problems, it is important to note its limitations. QAOA is an approximate algorithm, meaning it does not guarantee finding the exact optimal solution. The quality of the approximate solution depends on various factors, including the number of qubits, the depth of the quantum circuit, and the choice of parameters.

Furthermore, the implementation of QAOA requires a quantum computer, which is still in its early stages of development. Quantum computers are prone to errors, and the current technology has limited qubit coherence and gate fidelity. These limitations impact the performance and scalability of QAOA.


The Quantum Approximate Optimization Algorithm (QAOA) is an exciting quantum algorithm that has the potential to solve optimization problems more efficiently than classical algorithms. By combining classical optimization techniques with quantum computing, QAOA offers a new approach to tackling complex optimization problems in various fields.

While QAOA has its limitations, ongoing advancements in quantum computing technology hold promise for overcoming these challenges. As the field of quantum computing continues to evolve, QAOA is expected to play a significant role in solving real-world optimization problems and driving advancements in various industries


  • https://pennylane.ai/qml/demos/tutorial_qaoa_intro/
  • https://arxiv.org/pdf/1812.01041.pdf

By Anshul Pal

Hey there, I'm Anshul Pal, a tech blogger and Computer Science graduate. I'm passionate about exploring tech-related topics and sharing the knowledge I've acquired. With two years of industry expertise in blogging and content writing, I'm also the co-founder of HVM Smart Solution. Thanks for reading my blog – Happy Learning!

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