The Frobenius Anatomy of Distributed Quantum Protocols

Speaker: Alexis Toumi, email:

Tuesday, 10 January 2023, 14:00, Salle 1Z31

Abstract: Distributed consensus and leader election are two communication problems that quantum computers can solve in a deterministic way, while classical computers can only solve them probabilistically. These two quantum protocols can in fact be put in one-to-one correspondance with the GHZ and W states, the only two ways to entangle three qubits (up to LOCC, local operations and classical communication). In this talk, we will give an abstract formulation of quantum consensus and leader election in terms of spiders, also known as Frobenius algebras. In both cases, a single equation allows to create global entanglement from local interactions: spider fusion. We will conclude with some applications to quantum natural language processing (QNLP) where spiders allow to formalise the notion of anaphora and co-reference: we can compute a global meaning for text as the entanglement of local meanings for sentences.