for our next QM Talks@CBPF we receive Prof. Eduardo Mucciolo from the University of Central Florida. Although in USA at the moment, Eduardo keeps very strong ties with Brazil. He keeps collaborating with many people here, including Alfredo M. Ozorio de Almeida, our last speaker (see post below).
Recently Eduardo has been working on a very interesting connection between universal quantum computation and quantum chaos (articles here, and here). These works called our attention, and we take profit of his visit for the Brazilian Physical Society Meeting ENFMC 2015, to ask him to tell us about them. See the details below, and don’t miss this chance.
See you there.
Speaker: Eduardo Mucciolo (UCF)
Title: Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits and Many-Body Systems
Coordinates: room 601D, CBPF. 17.06, 16h30
Abstract: We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviate from Wigner-Dyson and the disentangling algorithm succeeds. The type of reversible gate (real permutation for universal classical computations or complex unitary operation for universal quantum computations) defines the symmetry class of the Wigner-Dyson ensemble governing the spectral statistics (orthogonal or unitary classes). These results open a new way to characterize irreversibility in quantum systems, regardless of whether they are governed by time-dependent or time-independent Hamiltonians. In particular, we show how entanglement spectrum statistics identify integrability (or lack thereof) in systems submitted to a quantum quench and how it is affected by many-body localization in disordered spin chains.