Related papers: Anyons and matrix product operator algebras
In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…
We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a…
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
A separable quantum state shared between parties $A$ and $B$ can be symmetrically extended to a quantum state shared between party $A$ and parties $B_1,\ldots ,B_k$ for every $k\in\mathbf{N}$. Quantum states that are not separable, i.e.,…
We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single…
Our investigation aims to study the specific role played by entanglement in the quantum computation process, by elaborating an entangled spin model developed within the 'hidden measurement approach' to quantum mechanics. We show that an…
This paper addresses the question of how categorical symmetries act on extended operators in quantum field theory. Building on recent results in two dimensions, we introduce higher tube categories and algebras associated to higher fusion…
With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…
Following a recent proposal of Richard Borcherds to regard fusion as the ring-like tensor product of modules of a {\em quantum ring}, a generalization of rings and vertex operators, we define fusion as a certain quotient of the (vector…
We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
Given a unitary fusion category, one can define the Hilbert space of a so-called ``anyonic spin-chain'' and nearest neighbor Hamiltonians providing a real-time evolution. There is considerable evidence that suitable scaling limits of such…
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…
Kauffman and Lomonaco explored the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G.…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…
The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of…
As is known, there exists an alternative, "non-matricial" way to present basic notions and results of quantum functional analysis (= operator space theory). This approach is based on considering, instead of matrix spaces, a single space,…