Related papers: Simulation of Anyons Using Symmetric Tensor Networ…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
The low-energy dynamics of two-dimensional topological matter hinges on its one-dimensional edge modes. Tunneling between fractional quantum Hall edge modes facilitates the study of anyonic statistics: it induces time-domain braiding that…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of…
The full exploitation of non-abelian symmetries in tensor network states (TNS) derived from a given lattice Hamiltonian is highly attractive in various aspects. From a theoretical perspective, it can offer deep insights into the…
Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…
We review the q-deformed spin network approach to topological quantum field theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the…
Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not…
Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
For non-abelian simple objects in a unitary modular category, the density of their braid group representations, the #P-hard evaluation of their associated link invariants, and the BQP-completeness of their anyonic quantum computing models…
We consider topological quantum memories for a general class of abelian anyon models defined on spin lattices. These are non-universal for quantum computation when restricting to topological operations alone, such as braiding and fusion.…
Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
It is known that describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, Bayesian tensor network (BTN) is proposed to efficiently capture the conditional probabilities of multiple…
Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension \chi of the bond indices that connect its tensors controls the…