Related papers: Efficient Preparation of Solvable Anyons with Adap…

We study a microscopic model of interacting fermions in a ladder setup, where the total number of particles is conserved. At a special point, the ground state is known and gives rise to a topological state of matter with edge modes obeying…

A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider…

One potential route toward fault-tolerant universal quantum computation is to use non-Abelian topological codes. In this work, we investigate how to achieve this goal with the quantum double model $\mathcal{D}(S_3)$ -- a specific…

The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by…

There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. ``Interpretability'' remains a concern: can we understand…

This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…

Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. In this work, we propose a simple method to design exact linear-depth parameterized quantum circuits…

We propose a family of order parameters to detect the symmetry fractionalization class of anyons in 2D topological phases. This fractionalization class accounts for the projective, as opposed to linear, representations of the symmetry group…

Anyon systems are studied in connection with several interesting applications including high $T_C$ superconductivity and topological quantum computing. In this work we show that these systems can be realized starting from directed polymers…

We consider the string-net model obtained from $SU(2)_2$ fusion rules. These fusion rules are shared by two different sets of anyon theories. In this work, we study the competition between the two corresponding non-Abelian quantum phases in…

Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum…

The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a…

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single)…

The eigenvalue structure of the quantum transfer matrix is known to encode essential information about the elementary excitations. Here we study transfer matrices of quantum states in a topological phase using the tensor network formalism.…

Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of…

We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant…

We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version…

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…