Physicists from the National University of Science and Technology MISIS and the Russian Quantum Center (RQC) have systematized modern approaches to implementing quantum algorithms using multidimensional quantum systems—qudits—and demonstrated how engaging additional energy levels of quantum carriers can simplify the execution of complex quantum operations and reduce their number compared to standard qubit-based schemes. Such approaches can improve the efficiency of quantum computing and bring the practical application of quantum algorithms closer in areas such as optimization, data processing, and the modeling of complex systems.
At the heart of quantum computing are qubits. Unlike a bit in a classical computer, which can be either “0” or “1,” a qubit can also exist in a superposition of states. When a qubit is measured, it “chooses” one of the states (0 or 1) with a probability determined by its superposition and then collapses into that state. Each qubit is encoded in the state of a specific physical system, such as an atom or a photon. Modern quantum processors still have a limited number of such elements and are sensitive to errors when performing complex tasks, which is why improving accuracy and reducing the number of computational operations remain key goals. In addition to qubits, there are more complex, multilevel units—qudits—which combine more states (three, four, or more) and can process more information. If researchers learn to control them effectively, these additional levels can be used to simplify computations without increasing the number of physical information carriers—atoms, ions, superconducting systems, and so on.
Researchers at MISIS have developed schemes in which the additional levels of qudits are engaged only during specific steps of an algorithm, after which the system returns to the standard qubit operating mode. This makes it possible to implement quantum algorithms more efficiently.
“We have shown how to simplify complex operations that are essential for most quantum algorithms. Typically, performing them requires many steps and additional elements, which increases the risk of errors. Using extra states already available in qudits allows us to reduce the number of steps needed to carry out such operations,” Alexey Fedorov, PhD, Director of the Institute of Physics and Quantum Engineering at MISIS.
The new approach is not tied to a specific technology and can be applied across various quantum platforms—from superconducting circuits to ionic and photonic systems. This makes the development universal and promising for the further advancement of quantum computing. The results help bring the practical use of quantum algorithms closer and enhance the efficiency of next-generation quantum devices.
“We deliberately focus on quantum algorithms represented in the form of qubit circuits, since this is how the overwhelming majority of quantum algorithms are described today. This allows us to directly link theoretical ideas with real hardware platforms and to show how qudits can be used without the need to completely rethink existing algorithms,” Anastasia Nikolaeva, PhD in Physics and Mathematics, Senior Researcher in the Quantum Information Technologies Group at the Russian Quantum Center and MISIS.
The article was published in Reviews of Modern Physics (Q1), which ranks among the top 1% of scientific journals by citation impact. According to the Scopus database, the journal’s percentile is 99—meaning its articles are cited more frequently than those in 99% of other journals. The journal ranks 13th among more than 49,000 titles across all fields of science.
“We analyzed a wide range of approaches to using qudits in quantum computing—both those developed in our previous studies and those proposed by other research groups. It was important for us not only to bring these results together, but also to highlight their strengths and weaknesses and to present the overall picture in a way that is clear to quantum hardware developers and to fellow theorists working on quantum algorithms,” Evgeny Kiktenko, PhD in Physics and Mathematics, Junior Scientific Director of the Quantum Information Technologies Group at the Russian Quantum Center.
The research was carried out as part of the MISIS strategic technological project “Quantum Internet” within the Priority 2030 program of the Russian Ministry of Science and Higher Education, with additional support from the Russian Science Foundation.
