# Freedman CMSA Seminar

## October 25, 2024 @ 2:30 pm - 5:30 pm

**Freedman CMSA Seminar**

***Note: via Zoom only***

**2:00-3:30 pm ET**

**Speaker: **Matt Hastings, Microsoft Quantum Program

**Title:** Invertible Phases of Matter and Quantum Cellular Automata: Dimensions One to Three

**Abstract:** A Quantum Cellular Automaton (QCA) is a *-automorphism of the algebra of local operators. While local quantum circuits provide one example of QCA, we are most interested in nontrivial QCA which are those which cannot be written as conjugation by a local quantum circuit. For systems in one and two spatial dimensions, all nontrivial QCA are shifts (i.e., translations by some amount), up to conjugation by a quantum circuit, but in three and higher dimensions, other examples are known. I’ll explain the relation between QCA and a certain “boundary algebra” of operators in one lower spatial dimension, and also the relation to invertible phases of matter on the boundary, and use this to explain and motivate some of these results in dimensions one through three.

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**3:30-4:00 pm ET**

**Break/Discussion**

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**4:00-5:30 pm ET**

**Speaker:** Lukasz Fidkowski, U Washington, Physics

**Title:** Invertible Phases of Matter and Quantum Cellular Automata: Higher dimensions

**Abstract:** We discuss the explicit construction of a non-trivial QCA in 3 dimensions, one which takes the form of multiplication by a discrete Chern-Simons functional in an appropriate basis for the Hilbert space. We relate the non-trivialness of the QCA to the fact that the Chern-Simons action is not the integral of a gauge invariant local quantity. One property of this QCA is that it creates a specific non-trivial time reversal symmetry protected topological (SPT) phase when acting on a non-trivial tensor product state. Motivated by this, we construct a general class of QCA in arbitrary dimensions based on time reversal protected SPTs, and conjecture a general correspondence between unoriented cobordism (which classifies such SPTs) and QCA.