Shang Liu

Oct 11, 2024 | dx.doi.org | Zhenzhen Wang |Chunming Wang |Shang Liu

It has come to our attention that a few images were inadvertently incorrectly placed in the originally published version of the article.The errors are mainly related to the PBS control group of Figure 1a, Figure 2h, and Figure 4c in the manuscript. The corrected images are demonstrated below and in the attached Supporting Information.

Jun 15, 2024 | nature.com | Shang Liu

AbstractRealizing topological orders and topological quantum computation is a central task of modern physics. An important but notoriously hard question in this endeavor is how to diagnose topological orders that lack conventional order parameters. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to detect nontrivial topological order from a ground state wave function, but is far from enough for fully determining the topological order.

Jun 5, 2024 | link.aps.org | Shang Liu

Realizing non-Abelian topological orders and their anyon excitations is an esteemed objective. In this work, we propose a novel approach towards this goal: quantum simulating topological orders in the doubled Hilbert space—the space of density matrices. We show that ground states of all quantum double models (toric code being the simplest example) can be efficiently prepared in the doubled Hilbert space; only finite-depth local operations are needed.

Jul 28, 2023 | link.aps.org | Chao Yin |Shang Liu

Abstract Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions, using two distinct mixed-state entanglement measures: the so-called computable cross-norm or realignment (CCNR) negativity, and the more well-known partial-transpose (PT) negativity.