English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Quantum phases of matter are resources for notions of quantum computation. Inthis work, we establish a new link between concepts of quantum informationtheory and condensed matter physics by presenting a unified understanding ofsymmetry-protected topological (SPT) order protected by subsystem symmetriesand its relation to measurement-based quantum computation (MBQC). The keyunifying ingredient is the concept of quantum cellular automata (QCA) which weuse to define subsystem symmetries acting on rigid lower-dimensional lines orfractals on a 2D lattice. Notably, both types of symmetries are treatedequivalently in our framework. We show that states within a non-trivial SPTphase protected by these symmetries are indicated by the presence of the sameQCA in a tensor network representation of the state, thereby characterizing thestructure of entanglement that is uniformly present throughout these phases. Byalso formulating schemes of MBQC based on these QCA, we are able to prove thatmost of the phases we construct are computationally universal phases of matter,in which every state is a resource for universal MBQC. Interestingly, ourapproach allows us to construct computational phases which have practicaladvantages over previous examples, including a computational speedup. Thesignificance of the approach stems from constructing novel computationallyuniversal phases of matter and showcasing the power of tensor networks andquantum information theory in classifying subsystem SPT order.

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter