Currently ongoing
Here you will find what I am currtenly working on. All the topics
you will find in this paged are linked by one key concept: Graphs in Quantum Computing.
If you think, for example, about Automata or Random Walks or Machine Learning in the classical setting,
they can all be described as Graphs (and a lot of other problems can be added to the list).
Such characterization led, in the decades, to a lot of very powerful results obtained using only graph theory
applied to a variety of different disciplines.
In the Quantum case, there is still some kind of gap. Encoding (Directed) Graphs to
obtain a Quantum Circuit is not a trivial task, Quantum (one way) Finite Automata
are not as expressive as their classical counterpart and Quantum Neural Networks are still
very young.
For this reason the question I am trying to answer is the following: are Graphs as powerful as in the classical case,
for the Quantum setting too?
2022
Graphs Encoding in Quantum Computing
My very first paper as a PhD student was about Graphs encoding in Quantum Computing.
It seems to be not a so trivial task because of the unitarity requirement of Quantum Computing.
In my github you can also find a python project (FREEQO) in which we implemented an encoder that given a directed Graph,
computes an unitary matrix that can be used as a circuit to traverse such graph.
2022
Quantum Finite Automata
I am working on the topics I introduced in my master thesis in order to publish a new
paper.
The aim of this research is to design a class of automata able to overcome the limitations of
state of the art Quantum Automata.
2022
Quantum Machine Learning
I got interested in this topic while practicing some demo using PennyLane.
I am studying both theoretical aspects and practical approaches.
For what concerns the theoretical results, I am interested in how the fundamental theorems in the classic case can be
translated into the quantum setting (like no free lunch theorem, or PAC learnability and so on).
Moreover, being a computer scientist, I am interested in the complexity analysis of QML techniques.
On the practical point of view, I always excercise using pennylane and their demos.
2022
Neural Network Compression
Always concerning graphs, during the past months, we tackled the Neural Network Reduction
problem (i.e. removing 'useless' neurons) using a theoretical approach. In particular,
we borrowed the notion of Lumpability from graph theory and devised
a polinomial time procedure that can reduce the size of NNs without reducing their accuracy.
2023
Quantum Circuit Synthesis
Once a Quantum Algorithm has been devised, we would be really happy if we could execute it.
This seems a stupid assumptions, but it is not. In the Quantum Circuit architecture, the problem
of turning a generic quantum algorithm (a really huge unitary matrix) into a sequence of smaller and executable
operations (smaller gates/unitaries), is not easy at all.
Such problem is called Quantum Circuit Synthesis and it is a really fervent research area nowadays.
Up to now, I have been working on the synthesis of circuits using the Clifford+T basis.