Research Interests

• Quantum chaos and quantum complexity:

  Although we still don’t know what quantum chaos is, recently there have been some steps towards the comprehension of chaos: the theory of quantum chaos is intimately connected to quantum pseudorandomness and quantum complexity. A unitary operator $U$ is chaotic if it is able to attain the value of $2k$ Out-Of-Time-Order correlators (OTOCs) reached by a (Haar) random unitary operator. While the Clifford group alone does not reproduce the Haar value for the general OTOCs -and thus cannot be considered chaotic - by doping Clifford circuits with a finite amount of non-Clifford gates one enforces transitions in quantum complexity by allowing such circuits in reaching the Haar value for higher order OTOCs. The goal of my research is to classify transitions in quantum complexity driven by the injection of non-Cliffordness in random quantum circuits.

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• Resource theory of magic:

  Magic is the quantum resource that allows quantum computers to attain the overwhelming computational advantage over classical computation. Without magic, a quantum computer cannot over-perform any classical computer. On the other hand, there exist quantum states possessing an extensive amount of magic, which still lack computational power. Such insufficiency is due to the absence of long-range quantum correlations, or entanglement. Indeed, it is the conjunction of magic and entanglement in a quantum state that makes that state a true resource for powerful quantum computation. My research aims to a deeper understanding of the synergy between magic and entanglement and its crucial role in the quantum advantage.

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