Department of Mathematical Methods for Quantum Technologies

The Department of Mathematical Methods for Quantum Technologies was established in Steklov Mathematical Institute in December 2018 on the base of the Laboratory of Mathematical Methods for Quantum Technologies, which was created in 2016. The Department was established with the goal of solving mathematical problems necessary for the development of quantum technologies. Quantum technologies exploit for practical purposes various specific properties of individual quantum systems such as photons, atoms, molecules. Examples of peculiar quantum properties are superposition of quantum states, quantum entanglement, Heisenberg uncertainty principle. Directions of quantum technologies include quantum information, quantum control, quantum computation and simulators, quantum cryptography, quantum metrology, etc. In this field, a number of mathematical problems arise which are investigated by the employees of the Department.

1. Performing of fundamental and applied research in the areas:
   • Open quantum systems;
   • Quantum control;
   • Quantum information;
   • Quantum cryptography;
   • Quantum complexity;
   • Quantum tomography;
   • Quantum teleportation;
   • Many-body quantum systems;
   • Adiabatic quantum computing;
   • Non-equilibrium quantum dynamics;
   • Holography & quantum information.
2. Development and reading of novel training courses on quantum technologies for students, graduate students and young scientists in the Research and Education Center of Steklov Mathematical Institute, within the master program «Mathematical Methods of Quantum Technologies» at the Department of Moscow Institute of Physics and Technology based at MIRAS «Methods of Modern Mathematics», in other Universities and Institutes, organization of workshops and conferences, popularization of quantum technologies.

Head of the Department — Alexander Pechen, Professor of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences, specialist in theory of open quantum systems, quantum control, quantum stochastic processes. In 2001 he graduated from Physics Department of M.V. Lomonosov Moscow State University. In 2004 received PhD degree at Steklov Institute. In 2005–2010 he worked at Princeton University (USA). He was visiting researcher in Weizmann Institute of Science (Israel) and Rome University «Tor Vergata» (Italy). In 2014 he obtained Doctor of Physical and Mathematical Sciences (Habilitation) degree in Steklov Institute. A. Pechen is a laureate of the Blavatnik Award (USA), Marie Curie Fellowship, and Moscow Government Award for Young Scientists. He is a member of the Dissertation Council of Steklov Institute, of the Editorial board of the journal Infinite Dimensional Analysis, Quantum Probability and Related Topics, and of the Academic Council of the International Association «The Association for Quantum Probability and Infinite Dimensional Analysis».

1. Project No. 17-11-01388 «Mathematical Methods for Problems of Quantum Technologies and Dynamics of Open Quantum Systems» (2017–2019; Principal investigator A.N. Pechen);
2. Project No. 17-11-01388-P «Mathematical Methods for Problems of Quantum Technologies and Dynamics of Open Quantum Systems» (prolonged; 2020–2021; Principal investigator A.N. Pechen);
3. Project No. 18-71-00074 «Using pseudorandom number generators in quantum cryptography» (2018–2019; Principal investigator D.A. Kronberg);
4. Project No. 20-71-10072 «The effect of interaction with the environment on the information properties of quantum channels» (2020–2022; Principal investigator D.A. Kronberg);
5. Project No. 22-11-00330 «Mathematical methods for control problems in quantum systems» (2022–2024; Principal investigator A.N. Pechen).

• Course by A.N. Pechen, E.O. Kiktenko and D.A. Kronberg "Mathematics of quantum technologies", October 8 – December 18, 2017.
• Course by A.S. Trushechkin and D.A. Kronberg "Mathematical foundations of quantum cryptography", September 8 – December 22, 2020.

Alexander Pechen, Vadim Petruhanov, Amir Arab, Quantum computers, cryptography and control, in the broadcast "Black holes. White spots" on TV channel "Culture", 28 and 30 May 2022. Video (in Russian)
Alexander Pechen, «Quantum technologies», Interview at NaukaPRO, October 4, 2020
Alexander Pechen, «Mathematics of quantum technologies», presentation at the General Meeting of the Branch of Mathematical Sciences, Russian Academy of Sciences (in Russian), 12 Nov 2018
Alexander Pechen, «Some topics in dynamics and control of quantum systems»,In the broadcast «Moscow. Territory of science» on radio station «Echo of Moscow» (in Russian), 29 May 2014 Listen
Dmitry Kronberg, «Quantum key distribution security and related problems», Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences, May 10, 2018
Dmitry Kronberg, «Quantum cryptography», Interview at NaukaPRO, November 29, 2020