Simulating the time-evolution of many-body quantum systems is a notoriously, exponentially hard problem, for which the possibility of a universal quantum computer raises promising perspectives. Indeed, as initially announced by Feynman (1982), it should be possible using a single quantum computer to simulate the evolution of any local quantum system, in what is now referred to as “digital quantum simulation” (DQS). The idea behind DQS is to approximate continuous-time dynamics by discrete Trotter steps of duration τ, each of which can be implemented by a simple sequence of quantum gates. While this should hold in principle for small enough τ, recent studies have shown that when τ is increased beyond a certain value, approximation errors become uncontrolled at large times due to the onset of quantum chaos, hence leading to a sharp “Trotter transition”.
In this talk I will contrast this picture with the case of an “integrable DQS”, where the simulated quantum many-body system and the discretized time evolution turn out to be integrable, that is, have an extensive number of conserved charges. Instead of becoming chaotic at large τ, such systems are governed by a different physics, and exhibit a rich structure of Trotter transitions of a new kind.
Based on :
Eric Vernier, Bruno Bertini, Giuliano Giudici, Lorenzo Piroli
Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions
arXiv:2212.06455
This will be as self-contained as possible, no prior notions about quantum integrability should be needed.
