Tower of Structured Excited States from Measurements

TL;DR

This paper introduces a log-depth measurement protocol using quantum phase estimation to efficiently generate and access highly entangled states, including excited states and Dicke states, in quantum many-body systems.

Contribution

It presents a novel measurement-based method to prepare structured excited states and high-weight Dicke states, expanding quantum state engineering capabilities.

Findings

Successfully prepares towers of excited states in various models.

Enables measurement of global observables without disturbing the system.

Facilitates access to states like the Arovas A state beyond traditional methods.

Abstract

Preparing highly entangled quantum states is a key challenge in quantum metrology and quantum information science. Measurements, especially those of global observables, offer a simple and efficient way to generate entanglement between subsystems when they are measured as a whole. We introduce a log-depth protocol leveraging quantum phase estimation to measure a global observable, such as total magnetization and momentum. We demonstrate its capability to prepare towers of structured excited states that are useful in quantum metrology; examples include quantum many-body scars in various models, including the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, the constrained domain-wall model, and the spin-$\frac{1}{2}$ and spin-$1$ XX chains. The same method is also applicable to preparing the Dicke states of high weight. In addition, we propose a protocol for momentum measurement that avoids disturbing the system, facilitating the preparation of states beyond the above construction, such as the Arovas $A$ state of the AKLT Hamiltonian. Our results expand the utility of measurement-based approaches to accessing highly entangled states in quantum many-body systems.