PIRSA:19100066

Quantum complexity, irreversibility, learnability and fluctuations.

Hamma, A. (2019). Quantum complexity, irreversibility, learnability and fluctuations. . Perimeter Institute. https://pirsa.org/19100066

Hamma, Alioscia. Quantum complexity, irreversibility, learnability and fluctuations. . Perimeter Institute, Oct. 10, 2019, https://pirsa.org/19100066 

          @misc{ pirsa_PIRSA:19100066,
            doi = {10.48660/19100066},
            url = {https://pirsa.org/19100066},
            author = {Hamma, Alioscia},
            keywords = {Other},
            language = {en},
            title = {Quantum complexity, irreversibility, learnability and fluctuations. },
            publisher = {Perimeter Institute},
            year = {2019},
            month = {oct},
            note = {PIRSA:19100066 see, \url{https://pirsa.org}}
          }

Alioscia Hamma University of Naples Federico II

DOI 10.48660/19100066
Collection
Talk Type Scientific Series
Subject

Abstract

Quantum complexity is a notion characterizing the universality of the entanglement arising from a quantum evolution. A universal evolution will result in a complex entanglement. At the same time, this also corresponds to small fluctuations and to unlearnability from the point of view of machine learning. All these aspects are connected to the different features of k-designs, which are under-samplings of the Hilbert space. 

We study the transition in complexity due to the doping of a quantum circuit by universal gates and show that the transition to complex entanglement can be obtained by just a single gate. 
These results are relevant for the notions of scrambling, quantum chaos, OTOCs and operator spreading.

We conjecture that the transition to 4−design, W-D and unlearnability are one and the same.