BEGIN:VCALENDAR VERSION:2.0 PRODID:-//linuxsoftware.nz//NONSGML Joyous v1.4//EN BEGIN:VEVENT SUMMARY:Multiistochastic operations and convolution channels for quantum s tates DTSTART:20240207T143000Z DTEND:20240207T160000Z DTSTAMP:20260622T030214Z UID:1b361932-7d0e-4faf-b2a7-bed18b953e92 SEQUENCE:1 CREATED:20240201T113132Z DESCRIPTION:The notion of convolution of two probability vectors can be ex tended to operationsdetermined by multistochastic tensors\, to describe Ma rkov chains of a higher order. Onthe other hand\, the idea of convolution lies in the centre of machine learningalgorithms for image processing: Con volutional Neural Networks. In my talk\, I will firstpresent the character ization of the probability eigenvectors of multi-stochastictensors\, corre sponding to fixed points of generalized Markov chains. Similar results wil lbe also obtained in the quantum case for multi-stochastic channels acting on mixedquantum states. Next\, I propose a quantum analogue of the convol ution\, based oncoherifications of tristochastic tensors\, defined for two arbitrary density matrices ofthe same size. Finally\, I will discuss poss ible applications of this notion to constructschemes of error mitigation o r as building blocks in quantum Convolutional NeuralNetworks.. LAST-MODIFIED:20240201T113132Z LOCATION:Sala de Seminários do DF\, Pavilhão de Física\, 2º piso URL:http://df.vps.tecnico.ulisboa.pt/pt/eventos/multiistochastic-operation s-and-convolution-channels-for-quantum-states/ X-ALT-DESC;FMTTYPE=text/html:

The notion of convo lution of two probability vectors can be extended to operationsdetermined by multistochastic tensors\, to describe Markov chains of a higher order. Onthe other hand\, the idea of convolution lies in the centre of machine l earningalgorithms for image processing: Convolutional Neural Networks.

In my talk\, I will firstpresent the characterization of the probab ility eigenvectors of multi-stochastictensors\, corresponding to fixed poi nts of generalized Markov chains. Similar results willbe also obtained in the quantum case for multi-stochastic channels acting on mixedquantum stat es.

Next\, I propose a quantum analogue of the convolution\, bas ed oncoherifications of tristochastic tensors\, defined for two arbitrary density matrices ofthe same size. Finally\, I will discuss possible applic ations of this notion to constructschemes of error mitigation or as buildi ng blocks in quantum Convolutional NeuralNetworks..

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