## Novel Algorithm can help design Medicines with Quantum Computing

Computational methods for designing medicines have greatly advanced alongside experimental approaches, significantly contributing to drug development by saving time and reducing costs. An interesting strategy for drug design involves finding the optimal chemical compound—from a large collection of molecule structures—that optimizes (minimizes or maximizes) a “figure of merit”. The figure of merit could be, for instance, the binding free energy, which gives the affinity of a molecule (or ligand) towards a protein. In this example, the goal would be identifying the molecular structure that optimizes the binding free energy.

However, determining the best medicine requires checking through a vast selection of molecular structure candidates. Although some relatively efficient classical optimization methods exist, it remains incredibly challenging and resource-consuming for classical computers to identify extremal values for large datasets. In fact, traditional classical methods do not search for the optimal molecular structure using a holistic approach. Instead, they use machine learning to train a model and then blindly predict the binding free energy for as many configurations as possible.

A novel computational method that helps find optimal solutions is called Extremal Learning. It combines machine learning techniques—which enable computers to learn from data and improve their accuracy to solve complex problems—with extremization methods.

Extremization is the art of finding an extremal value (maximum or minimum) of a model considering the parameters of the model. Researchers and engineers use extremization (sometimes also called optimization) techniques to decide on the most efficient use of their resources. In the drug discovery sector, it helps pharmaceutical companies find the best treatment for patients with a particular disease.

Inspired by classical extremal learning methods, researchers at PASQAL have created a quantum computing algorithm specially designed for extremization called Quantum Extremal Learning.

By embracing the principles of quantum physics, which are precisely the laws governing atomic and molecular behavior, this approach promises increased accuracy as compared to the classical solution and potential speed up when considering complex problems.

In their scientific preprint, the scientists show how their algorithm could be applied to drug design, including situations where datasets are too complex to be handled by classical computers. Let’s delve into the potential benefits of quantum computing in drug design through a particular example.

#### Designing medicines with Quantum Extremal Learning techniques, an example

Researchers in drug design typically aim to investigate the total energy of a molecule upon variations of its structure by replacing different chemical groups in targeted sites, as shown in the figure below.

In this example, we use the Xanthone molecule, which is known to have potential medicinal properties, including anti-viral, anti-tumor, and anti-inflammatory effects. The modified molecule will show a different binding free energy depending on which chemical group (R) is bound to each site. That means the binding free energy will change when changing each group R on each molecule site. The question we want to answer here is: What is the modified Xanthone molecule structure with the least binding free energy?

In real-life problems of this kind, scientists need to search for the optimal solution in a vast number of configurations. Classical methods that exhaustively search for the optimal combination are common due to the increased resource of classical computing power. However, these methods are inefficient and costly.

Due to their nature, quantum computers perform exceptionally well in tackling problems with a large number of combinations. By leveraging the principles of quantum physics, quantum processing units can process more information at the same time than classical computers. But how? Unlike the classical bit that can have values of either 1 or 0, the quantum bit, or qubit, can have both values 0 and 1 at the same time! A property called superposition. Then, we use a quantum phenomenon called entanglement, where we prepare the qubits to be strongly correlated to form a single quantum system. Quantum laws also allow us to prepare the states of the quantum system to have good control of the calculations. These properties, that are impossible to use in classical computing architectures, allow us to store loads of information simultaneously and to perform calculations in an extraordinarily efficient way.

Applying the quantum extremal learning algorithm to the xanthone molecule, we are able to leverage from superposition and entanglement to propose a good model that describes the relationship between the molecular structure and the binding free energy, and find the optimal structure, using only five qubits. This time, we allow only two substitute groups on each site, where each site is represented by a qubit, and we assign qubit values 0 and 1 to the possible R groups. Let’s take a closer look at this novel method.

#### Classical and quantum collaborating

The quantum extremal learning algorithm has two phases. In the first phase, we use quantum computing to propose a model that depends on an auxiliary tunable variable. Then, using classical computing, we tune this additional variable. We repeat the quantum calculation with the tuned variable and check if it needs more tuning. This is an iterative process: we repeat it until we find the best model that describes the problem.

Once we have a sufficiently accurate model, in the second phase, we use again our hybrid approach to find the extremal value of the total energy of the molecule, where we use the probabilistic nature of quantum computing to guide the process toward the optimal solution.

#### The future of drug design using quantum computing

Despite our understanding of biological systems and the advances in experimental and computational techniques, predicting a living organism’s response to medication remains a challenging task. However, making accurate predictions using computational methods helps reduce the time and cost involved in drug development.

At PASQAL we have demonstrated our capacity to successfully tackle pharmaceutical problems. Quantum extremal learning is a promising algorithm designed to help find extremal values (maximum or minimum value) problems that are too complex for classical computers, among others the ones that may push forward drug discovery. Advances in quantum computing will be of great value in the healthcare sector, enhancing our quality of life.

##### References

Varsamopoulos, S., et al, (2022). Quantum Extremal Learning. Preprint available: [2205.02807] Quantum Extremal Learning (arxiv.org)