PIRSA:23050148

Measurement Quantum Cellular Automata and Anomalies in Floquet Codes

Li, Z. (2023). Measurement Quantum Cellular Automata and Anomalies in Floquet Codes. Perimeter Institute. https://pirsa.org/23050148

Li, Zhi. Measurement Quantum Cellular Automata and Anomalies in Floquet Codes. Perimeter Institute, May. 17, 2023, https://pirsa.org/23050148 

          @misc{ pirsa_PIRSA:23050148,
            doi = {10.48660/23050148},
            url = {https://pirsa.org/23050148},
            author = {Li, Zhi},
            keywords = {Quantum Information},
            language = {en},
            title = {Measurement Quantum Cellular Automata and Anomalies in Floquet Codes},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {may},
            note = {PIRSA:23050148 see, \url{https://pirsa.org}}
          }

Zhi Li

Perimeter Institute for Theoretical Physics

Talk number
PIRSA:23050148
Collection
Talk Type
Subject
Abstract

We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently introduced Floquet topological codes. We define local reversibility in context of measurement circuits, which allows us to treat finite depth measurement circuits on a similar footing to finite depth unitary circuits. In contrast to the unitary case, a finite depth locally reversible measurement sequence can implement a translation in one dimension. A locally reversible measurement sequence in two dimensions may also induce a flow of logical information along the boundary. We introduce "measurement quantum cellular automata" which unifies these ideas and define an index in one dimension to characterize the flow of logical operators. We find a Z_2 bulk invariant for Floquet topological codes which indicates an obstruction to having a trivial boundary. We prove that the Hastings-Haah honeycomb code belong to a class with such obstruction, which means that any boundary must have either non-local dynamics, period doubled, or admits boundary flow of quantum information.

Zoom Link: https://pitp.zoom.us/j/96083249406?pwd=MnhYbTEyU05ybVdyUlE3UGZrdEhPdz09