Currently ongoing

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.

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.

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.

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.

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.

Quantum circuit routing and mapping are essential steps in compiling high-level quantum algorithms into executable instructions for real quantum hardware. Due to the limited connectivity between qubits in current quantum processors, quantum operations often cannot be executed directly on the hardware as described in the abstract circuit. Routing addresses this challenge by inserting additional operations—such as SWAP gates—to move qubits into adjacent positions, while mapping refers to assigning logical qubits from the circuit to physical qubits on the device. Efficient routing and mapping are critical for minimizing circuit depth and gate errors, both of which directly affect the fidelity of quantum computations. My research explores optimization techniques and algorithms for improving the performance of these compilation steps, with a focus on making quantum software more hardware-aware and scalable.