相关论文: Braid Group, Temperley--Lieb Algebra, and Quantum …

We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is…

In this work we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially we present an general formulation through elements of left minimal ideals in tensor…

Federated learning enables collaborative model training across multiple clients without sharing raw data, thereby enhancing privacy. However, the exchange of model updates can still expose sensitive information. Quantum teleportation, a…

We study homological representations of mapping class groups, including the braid groups. These arise from the twisted homology of certain configuration spaces, and come in many different flavours. Our goal is to give a unified general…

The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $\TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector…

In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

Distributed quantum computing supports combining the computational power of multiple quantum devices to overcome the limitations of individual devices. Circuit cutting techniques enable the distribution of quantum computations via classical…

It is well-known that maximally entangled states such as the Greenberger-Horne-Zeilinger (GHZ) states, with the Bell states as the simplest examples, are widely exploited in quantum information and computation. We study the application of…

Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for…

In this work, we have expounded the communication procedure of quantum systems by means of process algebra. The main objective of our research effort is to formally represent the communication between distributed quantum systems. In this…

Quantum physics education at the upper-secondary level traditionally follows a historical approach, rarely extending beyond early 20th-century ideas, leaving students unprepared for comprehending modern quantum technologies central to…

This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the…

Future quantum internet applications will derive their power from the ability to share quantum information across the network. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the…

Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…

Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum…

We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the…

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of…

This expository article supplies the mathematical background underpinning the braid representation calculator introduced in arXiv:2212.00831; those representations describe the sets of logic gates available to a topological quantum computer…

Quantum teleportation is a fundamental ingredient for quantum information science and technology. In particular, the ability to perform quantum teleportation between quantum systems of different natures and encoding types is crucial for…