Quantum complexity, irreversibility, learnability and fluctuations.

PIRSA ID: 19100066
Series: Perimeter Institute Quantum Discussions
Event Type: Seminar
Scientific Area(s):
Other
End date:
Speaker(s):
  • Alioscia Hamma, University of Massachusetts Boston - Department of Physics
October 10, 2019 at 4:00 PM Time Room

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.