PIRSA:14090028

Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits

Mucciolo, E. (2014). Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits. Perimeter Institute. https://pirsa.org/14090028

Mucciolo, Eduardo. Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits. Perimeter Institute, Sep. 30, 2014, https://pirsa.org/14090028 

          @misc{ pirsa_PIRSA:14090028,
            doi = {10.48660/14090028},
            url = {https://pirsa.org/14090028},
            author = {Mucciolo, Eduardo},
            keywords = {Condensed Matter},
            language = {en},
            title = {Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {sep},
            note = {PIRSA:14090028 see, \url{https://pirsa.org}}
          }

Eduardo Mucciolo University of Central Florida

DOI 10.48660/14090028
Collection
Talk Type Scientific Series
Subject

Abstract

We show that for a system evolving unitarily under a stochastic quantum circuit, the notions of irreversibility, universality of computation, and entanglement are closely related. As the state of the system evolves from an initial product state, it becomes increasingly entangled until entanglement reaches a maximum. We define irreversibility as the failure to find a circuit that disentangles a maximally entangled state. We show that irreversibility occurs when maximally entangled states are generated with a quantum circuit formed by gates from a universal quantum computation set. We find that irreversibility is also associated to a Wigner-Dyson statistics in the fluctuations of spacings between adjacent eigenvalues of the system’s reduced density matrix. In contrast, when the system is evolved with a non-universal set of gates, the statistics of the entanglement spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. We discuss how these findings open a new way to characterize non-integrability in quantum systems.