Precise measures of the complexity of states and operators in Quantum Field Theories and applying them in the holographic correspondence and quantum gravity models will be the subject of the research conducted by Prof. Paweł Caputa from the UW’s Faculty of Physics as part of the Consolidator Grant, given by the European Research Council.

Prof. Paweł Caputa’s project “Quantum Complexity from Quantum Field Theories to Quantum Gravity” was funded to the amount of over €1.8 mln.


Quantum Field Theories (QFTs) are the best models to describe nature, from new phases of matter to black holes. Still, to simulate them efficiently, one needs to know the best ways to create interesting quantum states from the basic building blocks used in computation. This problem necessitates a precise definition of “quantum complexity”, and its provision is one of the most urgent problems at the interplay between theoretical physics, quantum information and computation.


“We want to understand what is hard and what is easy in the quantum world. We are also curious to know what the laws of physics might look like inside black holes,” Prof. Paweł Caputa says. “To be exact, the project aims to develop precise measures of the complexity of states and operators in QFTs and apply them in the holographic correspondence and quantum gravity models,” the researcher explains.

The video is available at the University’s YouTube channel.

Interdisciplinary project

The new tools developed by the research team will allow them to chart the complexity frontier of quantum many-body systems, help to understand thermalisation, and shed light on the behaviour of matter near cosmological singularities relevant to our early universe.


“This interdisciplinary project brings methods and intuition from information theory and quantum computing to many-body physics and quantum gravity,” Prof. Caputa emphasises.


The applied methods will involve new definitions of complexity in quantum mechanics, analytical and numerical computations in free and interacting QFTs, including integrability, conformal symmetry, Krylov basis, Arnoldi algorithm, and finally, the AdS/CFT correspondence and quantum gravity.


Prof. Caputa’s team will include three doctoral candidates and three postdocs, who will collaborate with the researcher on the main parts of the projects, such as synthesising and developing complexity measures for QFTs, formulating the complexity measures in exact holographic models, and applying them to better understand physics behind black-hole horizons and spacetime singularities.


The project will start in autumn 2024 and will last for sixty months.

Prof. Paweł Caputa works at the Faculty of Physics, University of Warsaw. His main research interest lies in theoretical physics, in particular, quantum information and complexity in quantum field theories, quantum gravity and the AdS/CFT correspondence. Prof. Caputa was awarded a doctoral degree at the Niels Bohrs Institute in Copenhagen and conducted postdoctoral research at the University of the Witwatersrand in Johannesburg, Kyoto University and at the Nordic Institute for Theoretical Physics (NORDITA) in Stockholm. Subsequently, as an assistant professor he became a member of the Simons Foundation’s collaboration “It from Quibit”. Currently, he still cooperates with the Yukawa Institute in Kyoto (as an affiliate member) and a Japanese research team, conducting the Extreme Universe project. Since 2020, he has been the head of the teams implementing the Polish National Agency for Academic Exchange project titled “Polish Returns” and the National Science Centre SONATA BIS grant at the University of Warsaw.