# Quantum Computing Applications - Optimization

Optimization problems are found in numerous industries. Here are just a few examples:

**Portfolio optimization**. A money manager has a certain amount of money to invest. What is the optimal allocation of these funds?**Route optimization**. A FedEx truck needs to deliver 50 packages. What is the optimal route to deliver the packages?**Airport security**. An airport wishes to install security cameras to watch over all corners in the airport. What is the optimal arrangement of cameras that achieves this?

Each optimization has some definition of what constitutes an optimal solution, and a set of constraints. Let’s explore the optimal solution and some possible constraints for each example:

**Portfolio optimization.** The money manager might seek the highest return with the lowest risk. The constraint might be, for instance, not investing more than 5% of the portfolio in any single asset.

**Route optimization.**The FedEx truck might want to complete the deliveries in the minimum amount of time. Alternative definitions of the optimal solution, instead of the shortest delivery time, might be the lowest-cost route, considering fuel and toll charges, or the route that generates the lowest carbon footprint. The constraint might be not to travel on certain residential roads before 8 AM.**Airport security.** The airport might wish to cover all corridors with the smallest number of cameras. A constraint might be that there must be at least one camera in each concourse.

It’s easy to see how optimization problems can become exceptionally complex. The FedEx truck with 50 stops has about 30 vigintillion

(that’s 3 x 10^64) possible options. Even if the optimization can be completed in a reasonable amount of time, it might need to be redone at a moment’s notice: There is a major traffic jam on the route, the price of an asset has dropped making it more attractive for purchase, etc.

But when problems are hard, solving them could provide a big reward. A logistics company that saves 15% on fuel costs because of optimized routing can increase its profits or grow its market share. An optimal portfolio is good for the customer, the portfolio manager, and her employer.

The difficulty of solving these problems and the payoff of getting the best answers are key reasons that companies are considering quantum computing. To put this in a financial context, the Boston Consulting Group recently estimated that there is between $110-210B of value that can be unlocked in solving optimization problems using quantum computers.

## Here's how it looks with Classiq:

Take the airport security problem. This type of problem is known as a “max vertex cover” problem.

The user specifies the configuration or floor plan of the airport and the number of cameras they want to use, and Classiq’s synthesis engine sets up the mathematics of the problem.

In technical terms, the user provides a weighted edge graph and size of the vertex cover. Classiq provides a function that defines the problem, constraints, and solution. The problem is then solved using QAOA (Quantum Approximate Optimization Algorithm). This is a hybrid algorithm - a quantum portion (quantum cost function encoding the solution or the expectation value we want to optimize, a quantum mixer function to explore each possible solution, a quantum ansatz or parametrized initial state), and a classical optimization portion (in our case, we use the Pyomo package).

Here we specify a star graph with three outer nodes like pictured below. For convenience, we marked each node with a number. If we only have *one* camera, what position would cover all areas of the airport?

Once we generate the circuit, an interactive circuit pops up in a new window. The circuit’s structure is clearly seen, and we can dive deeper into any part of the circuit by clicking the plus icon in the top left corner.

When we execute this circuit with the QAOA and print the results, we get this solution (chosen because the algorithm works to minimize the ‘cost’ function).

The list corresponds to the potential camera locations, so position 0, the center node, should have a camera.

Interested in seeing what the Classiq platform can deliver for your organization? Contact us to schedule a demo

Optimization problems are found in numerous industries. Here are just a few examples:

**Portfolio optimization**. A money manager has a certain amount of money to invest. What is the optimal allocation of these funds?**Route optimization**. A FedEx truck needs to deliver 50 packages. What is the optimal route to deliver the packages?**Airport security**. An airport wishes to install security cameras to watch over all corners in the airport. What is the optimal arrangement of cameras that achieves this?

Each optimization has some definition of what constitutes an optimal solution, and a set of constraints. Let’s explore the optimal solution and some possible constraints for each example:

**Portfolio optimization.** The money manager might seek the highest return with the lowest risk. The constraint might be, for instance, not investing more than 5% of the portfolio in any single asset.

**Route optimization.**The FedEx truck might want to complete the deliveries in the minimum amount of time. Alternative definitions of the optimal solution, instead of the shortest delivery time, might be the lowest-cost route, considering fuel and toll charges, or the route that generates the lowest carbon footprint. The constraint might be not to travel on certain residential roads before 8 AM.**Airport security.** The airport might wish to cover all corridors with the smallest number of cameras. A constraint might be that there must be at least one camera in each concourse.

It’s easy to see how optimization problems can become exceptionally complex. The FedEx truck with 50 stops has about 30 vigintillion

(that’s 3 x 10^64) possible options. Even if the optimization can be completed in a reasonable amount of time, it might need to be redone at a moment’s notice: There is a major traffic jam on the route, the price of an asset has dropped making it more attractive for purchase, etc.

But when problems are hard, solving them could provide a big reward. A logistics company that saves 15% on fuel costs because of optimized routing can increase its profits or grow its market share. An optimal portfolio is good for the customer, the portfolio manager, and her employer.

The difficulty of solving these problems and the payoff of getting the best answers are key reasons that companies are considering quantum computing. To put this in a financial context, the Boston Consulting Group recently estimated that there is between $110-210B of value that can be unlocked in solving optimization problems using quantum computers.

## Here's how it looks with Classiq:

Take the airport security problem. This type of problem is known as a “max vertex cover” problem.

The user specifies the configuration or floor plan of the airport and the number of cameras they want to use, and Classiq’s synthesis engine sets up the mathematics of the problem.

In technical terms, the user provides a weighted edge graph and size of the vertex cover. Classiq provides a function that defines the problem, constraints, and solution. The problem is then solved using QAOA (Quantum Approximate Optimization Algorithm). This is a hybrid algorithm - a quantum portion (quantum cost function encoding the solution or the expectation value we want to optimize, a quantum mixer function to explore each possible solution, a quantum ansatz or parametrized initial state), and a classical optimization portion (in our case, we use the Pyomo package).

Here we specify a star graph with three outer nodes like pictured below. For convenience, we marked each node with a number. If we only have *one* camera, what position would cover all areas of the airport?

Once we generate the circuit, an interactive circuit pops up in a new window. The circuit’s structure is clearly seen, and we can dive deeper into any part of the circuit by clicking the plus icon in the top left corner.

When we execute this circuit with the QAOA and print the results, we get this solution (chosen because the algorithm works to minimize the ‘cost’ function).

The list corresponds to the potential camera locations, so position 0, the center node, should have a camera.

Interested in seeing what the Classiq platform can deliver for your organization? Contact us to schedule a demo

## 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.

If you would like to suggest a guest for the podcast, please contact us.