Optimal steering of matrix product states and quantum many-body scars

TL;DR

This paper develops and compares control strategies for quantum many-body systems using matrix product states, demonstrating improved methods for state preparation, entanglement steering, and scar generation in complex models.

Contribution

It introduces a leakage minimization control approach for MPS, outperforming counter-diabatic methods, and applies it to generate quantum scars in various models.

Findings

Leakage-based control outperforms counter-diabatic methods.

Successful construction of quantum scars in Floquet and driven Ising models.

Demonstrated entanglement steering in generalized PXP model.

Abstract

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states~(MPS). We compare counter-diabatic and leakage minimization approaches to the so-called local steering problem, that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS state in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counter-diabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally we apply our leakage minimization approach to construct quantum scars in the periodically driven non-integrable Ising model.