Quantum technologies build upon quantum mechanics, which describes the nature at the level of elementary particles. Quantum systems are already being used in cryptography to ensure data security, in managing traffic flows in world capitals, and in training artificial intelligence. They have an enormous potential of medical applications: from the development of new drugs and vaccines to decoding the genome.
– Quantum systems could fundamentally transform the ways and speed of transmitting and processing large volumes of information. Take, e.g., the well-known seating arrangement problem: there are different ways to seat eight guests at a table, and one of them is optimal. A classical computer would process all possible permutations sequentially, which would take millions of years. A quantum computer would accomplish the task in a single step, – explained Maria Makarova, Junior Researcher of the Institute of Applied Mathematical Researcher (IAMR) KarRC RAS.
Maria Makarova, Junior Researcher of the Institute of Applied Mathematical Research KarRC RAS. Courtesy photo
However, the era of quantum computers is not there yet. Physicists, mathematicians, and computer scientists from various countries work to improve their performance.
The basic unit of information in quantum computing is called a qubit. It is analogous to the bit, which classical computing uses to make software in our gadgets work. There is a fundamental difference, however, which is responsible for the huge performance gap between classical and quantum systems. While a bit can only assume one of two values – either 0 or 1 (hence the binary system that many of us know from school), a qubit exists simultaneously in a superposition of all possible states: both 0 and 1, and numerous variations thereof. This allows the system to run thousands of times more operations in a single step than conventional software.
The number of qubits in quantum computer storage is limited. The most powerful one in Russia was developed at the Lebedev Physical Institute RAS and contains 50 qubits. Physically, these particles are so far rather unstable: e.g., they are highly sensitive to their environment. Changes in temperature and other factors can lead to a loss of quantum properties and a degradation in the accuracy and stability of computations. In general, too, the complexity of the system and its units inevitably leads to errors.
The commands to perform a certain operation are delivered to qubits via micro-devices called gates. Qubits and gates form quantum circuits, which ultimately fulfill the required task.
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– On top of other limitations, quantum systems have a very specific architecture, i.e. not any combinations of qubit arrangement are possible. Often, the "nearest-neighbor architecture" is used, meaning that we can only perform operations with qubits that are physically close to each other. If we need to involve qubits that are distant from one another, swap operations are used, which transpose the particles. However, the more swap operations are employed, the higher the probability of error. That is why we strive to minimize their number and optimize the quantum circuit in terms of the number of swap operations, – explained Maria Makarova.
To achieve this, scientists use the qubit reordering approach. Although quantum computers are involved, this process typically relies on classical, semiconductor-based hardware and software. Within the new method, the authors of the paper propose using not classical, but quantum hardware, specifically, a quantum annealing device. The evolution of the system during quantum annealing is described by an equation by solving which we find the optimal arrangement of qubits with minimal rearrangement. The method was named by analogy with metallurgy, where annealing is a type of thermal treatment where an alloy is heated to a certain temperature and then allowed to cool slowly. As the metal had cooled down, the arrangement of particles attains a steady state with minimal energy.
– It is believed that any physical system tends toward a lowest-energy state. In quantum annealing, the system also undergoes slow changes but ultimately remains in its ground state. Our task is to select a configuration that requires less energy to achieve this, – noted the scientist.
The qubit reordering approach and the quantum annealing method have long been known and widely used in quantum computing. The novelty of the research by mathematicians from the IAMR KarRC RAS is that they are co-applied to optimize quantum circuits and thus to minimize errors and enhance computing performance.
The scientists tested the new method on a cloud-based D-Wave quantum computer (Canada). The results showed that the optimization has indeed reduced the number of swap operations and increased the rate of their successful execution.
– Numerical experiments show that the results of such optimization match those of classical software, and in some cases perform even better. We have thus demonstrated the potential of quantum annealing-based machines for optimizing quantum circuits, which makes our work methodologically innovative, – summarized Maria Makarova.
Article on quantum chain optimization was published in Lobachevskii Journal of Mathematics
A graduate of Petrozavodsk State University, in 2025 she received postgraduate diplomas from two countries at once: she completed a postgraduate program remotely at the University of Trento (Italy), where she successfully defended her doctoral dissertation in April, and in person at the Karelian Research Centre RAS. Her specialization is unique for Karelia.
– I became involved with the topic of quantum computing after completing my university studies and upon entering the University of Trento, under the supervision of Professor Enrico Blanzieri from the Department of Information Engineering and Computer Science. This is a relatively new field, even in global science, which appealed to me a lot. I had to learn the subject from the ground up. Currently, we are working at the intersection of mathematics and computer science – seeking to optimize quantum circuits, which are hard-to-construct yet universal models that facilitate any sort of computation, – shared Maria Makarova.
The article “Quantum circuit optimization via graph partitioning by quantum annealing” made Maria Makarova the winner of the KarRC RAS Young Scientists Contest in the STEM category.
