Chiara Paletta (Univ. of Ljubljana)

Is a Given Quantum Circuit Integrable? From Detection to Construction

Quantum circuits can efficiently simulate the dynamics of many-body quantum systems that would otherwise be difficult to access by using classical computers. A special class of these, known as integrable quantum circuits, is defined by an infinite set of commuting conserved charges, which constrain the dynamics and enable analytical calculation of correlation functions. Central open questions in the fields of statistical physics and integrability include: Is a given quantum circuit integrable? And how can we systematically construct integrable quantum circuits? In this talk, I will address these questions in the context of Yang-Baxter integrable models. The presentation will be structured in three parts: 1) I will begin with a brief review of quantum integrability and quantum circuits, highlighting the link between them. 2) I will introduce an efficient algorithm to determine whether a given circuit is integrable, along with the algebraic structures needed to understand its integrability; 3) Finally, I will discuss the Yang-Baxter integrability of a deformation of Rule 54, a classical cellular automaton that can be embedded within the quantum circuit framework. This talk is based on 2406.12695 (with T. Prosen) and 2503.04673 (with U. Duh, B. Pozsgay, L. Zadnik)