PIRSA:21110002

Video URL

https://pirsa.org/21110002

Topological aspects of quantum cellular automata in one dimension

Gong, Z. (2021). Topological aspects of quantum cellular automata in one dimension. Perimeter Institute for Theoretical Physics. https://pirsa.org/21110002

Gong, Zongping. Topological aspects of quantum cellular automata in one dimension. Perimeter Institute for Theoretical Physics, Nov. 03, 2021, https://pirsa.org/21110002 

          @misc{ scivideos_PIRSA:21110002,
            doi = {10.48660/21110002},
            url = {https://pirsa.org/21110002},
            author = {Gong, Zongping},
            keywords = {Quantum Information},
            language = {en},
            title = {Topological aspects of quantum cellular automata in one dimension},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {nov},
            note = {PIRSA:21110002 see, \url{https://scivideos.org/index.php/pirsa/21110002}}
          }

Zongping Gong Max Planck Institute of Quantum Optics

Talk numberPIRSA:21110002
DOI10.48660/21110002
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Quantum cellular automata (QCA) are unitary transformations that preserve locality. In one dimension, QCA are known to be fully characterized by a topological chiral index that takes on arbitrary rational numbers [1]. QCA with nonzero indices are anomalous, in the sense that they are not finite-depth quantum circuits of local unitaries, yet they can appear as the edge dynamics of two-dimensional chiral Floquet topological phases [2].

In this seminar, I will focus on the topological aspects of one-dimensional QCA. First, I will talk about how the topological classification of QCA will be enriched by finite unitary symmetries [3]. On top of the cohomology character that applies equally to topological states, I will introduce a new class of topological numbers termed symmetry-protected indices. The latter, which include the chiral index as a special case, are genuinely dynamical topological invariants without state counterparts [4].

 

In the second part, I will show that the chiral index lower bounds the operator entanglement of QCA [5]. This rigorous bound enforces a linear growth of operator entanglement in the Floquet dynamics governed by nontrivial QCA, ruling out the possibility of many-body localization. In fact, this result gives a rigorous proof to a conjecture in Ref. [2]. Finally, I will present a generalized entanglement membrane theory that captures the large-scale (hydrodynamic) behaviors of typical (chaotic) QCA [6].

References:
[1] D. Gross, V. Nesme, H. Vogts, and R. F. Werner, Commun. Math. Phys. 310, 419 (2012).
[2] H. C. Po, L. Fidkowski, T. Morimoto, A. C. Potter, and A. Vishwanath, Phys. Rev. X 6, 041070 (2016).
[3] Z. Gong, C. Sünderhauf, N. Schuch, and J. I. Cirac, Phys. Rev. Lett. 124, 100402 (2020).
[4] Z. Gong and T. Guaita, arXiv:2106.05044.
[5] Z. Gong, L. Piroli, and J. I. Cirac, Phys. Rev. Lett. 126, 160601 (2021).
[6] Z. Gong, A. Nahum, and L. Piroli, arXiv:2109.07408.