The time evolution of quantum states is a fundamental challenging computational task. Being able to simulate this evolution offers the opportunity to investigate experimental systems that are far from equilibrium. This has gained particular importance recently, thanks to the emergence of highly controllable platforms like neutral atoms and trapped ions.
Regrettably, when attempting to perform time evolution calculations of such systems on classical computers using the state-of-the-art matrix-product states (MPS) method, a significant hurdle arises. This issue is characterized by a memory demand that grows exponentially with the duration of the evolution, limiting our ability to simulate long-time processes.
In response to this challenge, researchers from the Neupert group at the University of Zurich, the Smith group at the University of Nottingham, and the Pollmann group at Technische Universität München have devised a quantum adaptation of the MPS method. This innovative approach enables the time evolution of infinite one-dimensional quantum systems on a finite quantum device. Crucially, they have observed that the digital gate structure of quantum operations allows for the storage of a quantum state with a linear number of parameters (in evolution time), which alleviates the existing problem in classical computations.