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# Professor Kourtis develops an advanced tool for the simulation of quantum circuits

Example of a near-optimal contraction tree for a small tensor network.

Photo :How is the quantum advantage frontier defined? Is it possible to optimize the simulation of quantum and classical calculations? Professor Stefanos Kourtis discusses these questions in his article Hyper Optimized Tensor Network Contraction, published recently in Quantum, an open-access journal for quantum science. His research, which has already received several citations from the Google team, also solves one of the most difficult combinatorial enumeration problems and promises practical and intradisciplinary repercussions.

**Tensor Networks and Entanglement Physics for the Simulation of Quantum Circuits**

Professor Kourtis’s publication concerns a method for simulating both quantum and classical calculations using tensor networks. This tool is a language that expresses calculations, a list of operations required to complete a simulation. The order of these operations, however, can make a vast difference in performance. Indeed, tensor networks express a list of tasks to be completed, without specifying the order. Just like following a grocery list, the order of items collected will affect the time it takes to complete the errand, just as the order of operations will affect the time it takes to complete a simulation. Thus, Professor Kourtis’s work sought, in an algorithmic way, the most efficient orders to evaluate tensor networks.

Recently, Google defined the time required to complete the classical simulation of a specific quantum computation to be around 10,000 years. Professor Kourtis’s algorithms show just the opposite: he estimates it to be a few hundred days, a phenomenal difference in the quantum computing simulation.

“What we found is that by using methods inspired by the physics of the N-body problem, we can find orders that are more effective than we originally imagined. Among the practical benefits is the simulation of quantum circuits, recently implemented by the Google team. Our research shows that we can do this simulation much faster and more efficiently than what Google had estimated,” says Professor Kourtis.

Indeed, the publication already has several citations, especially by the team at Google which uses the algorithms developed by Professor Kourtis’s team as an advanced method for the classical simulation of quantum circuits. A team of researchers in Beijing has also implemented a classic simulation of Sycamore circuits on supercomputers using Professor Kourtis’s techniques.

What makes these algorithms more beneficial than others? According to the theoretical physicist, the physics of entanglement, although fundamental, led to the performance of his algorithm: “The main obstacle in the use of tensor networks is the increase of memory needed to store tensors, an increase that represents the growth of quantum entanglement during the quantum computation simulated. This increase leads to a severe loss of performance. So, if we can identify the order that avoids most of the entanglement, the simulation will be more efficient. This is the element that directed the research, and it is for this reason that we arrived to an almost optimal solution.”

**A Universal Prelude**

This publication announces the research that will be carried out within the Chair in Quantum Computing. Created at the end of 2020 and funded for the most part by the ministère de l’Économie et de l’Innovation du Québec (MEI), Professor Kourtis’s Chair aims to develop new methods in quantum computing.

“Tensor networks are an interdisciplinary research field, and our work in my group combines ideas from artificial intelligence, data science, quantum physics, quantum information, and also theoretical computer science. This combination can lead to significant benefits, and this publication is a proof-of-concept of precisely that fact. If we can optimize the efficiency of tensor networks, the Chair can have a very broad impact in all these areas of research,” adds Professor Kourtis.

The Chair’s next project has several components, relating to the research carried out within the framework of this article:

“The first is the study of quantum correcting codes in multiple qubits using the same tool. The next step to be demonstrated is controlled approximation strategies in similar simulations.

Then, we will continue to carry out quantum computing simulations, in order to better define the quantum advantage frontier, which is a very relevant question, since we depend on classical computers to simulate quantum computing.

Another aspect that the Chair will pursue is to use tensor network methods more directly in the field of machine learning, in collaboration with a researcher from Mila, the Quebec AI Institute in Montreal, and with a student arriving this fall,” specifies the Chairholder.

The research carried out by the Chair contributes to the development of tools and knowledge in the field of quantum computation by providing innovative solutions to modern challenges, supporting Sherbrooke’s innovation zone project in quantum science. “Often, innovation depends on computation and their efficiency, so if we can develop tools that accelerate computation, we can accelerate innovation,” concludes Professor Kourtis.