Research project is (co) funded by the Slovenian Research Agency.
UL Member: Faculty of Mathematics and Physics
Code: J1-70049
Project:Dynamics of many-body quantum circuits
Period: 1. 3. 2026 - 28. 2. 2029
Range per year: 0,83 FTE, category: C
Head: Marko Žnidarič
Research activity: Natural sciences and mathematics
Project description:
Physics is an endeavor where theoreticians propose theories -- a set of as simple as possible rules describing the way Nature works -- which are then tested in experiments. It is therefore of utmost importance to understand what are the properties, for instance dynamics, that results from a given set of rules. For instance, what are dynamical properties of a system described by a specific Hamiltonian. In the project we shall study dynamical properties of many-body quantum systems whose evolution is determined by quantum circuits, that is the language of quantum computation.
The question of dynamics is, of course, not new. But so-far it is well understood only for classical systems and for single-particle quantum systems. In classical dynamics one has a well defined notions like integrability, ergodicty, or chaos, that classify systems according to their dynamical properties, covering the whole spectrum from being predictable for integrable systems, to being unpredictable for chaotic. How to define chaos in quantum systems is a bit trickier. For single-particle systems there is the famous quantum chaos conjecture saying that systems whose classical counterpart is chaotic will display level statistics compatible with random matrix theory. In particular, there will be a statistical repulsion between nearest eigenenergies. In many-body quantum systems, while one can in principle use the same criterion, this is unsatisfactory because the nearest eigenenergies are exponentially close (in system length), and therefore only matter for behavior on exponentially long timescales that are physically and experimentally irrelevant. Mathematically speaking, the limits of system size going to infinity (the thermodynamic limit) and time to infinity do not commute.
With a rapid progress in near intermediate scale quantum computation (NISQ), where studying long times is harder than studying large systems, the problem is even more accute. In the project we plan to study how to define different notions of dynamical regimes in many-body quantum systems that will matter on timescales that are polynomial in system size. We want to be able to address questions like what is really quantum chaos in a many-body setting.
We propose a new approach, namely, instead of focusing on unitary evolution in an exponentially large Hilbert space, we are going to focus on non-unitary evolution on smaller space that is relevant for measurable observables. Doing that the focus is shifted from the spectral properties of unitary operators to the spectral properties of non-unitary operators. In particular, different dynamical regimes can be classified according to the spectral gap and its scaling. Furthermore, the method is very versatile and powerful not just for chaotic systems but can also be used to study integrable quantum systems.
