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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Quantum cellular automata (QCA) are discrete models of space and timehomogeneous quantum field theories (QFTs) and regarded as natural candidatesfor quantum simulation. Description of a QCA over the separable Hilbert spaceof finite, unbounded configurations (UFC Hilbert space) with unitary stateevolution is the {\it Schr\"{o}dinger template}, and over the incompleteinfinite tensor product algebra (ITPA) with evolution by algebra automorphismis the {\it Heisenberg template}. Whether every Heisenberg template admits anequivalent Schr\"{o}dinger template is a foundational question, and one thathas persisted as an open problem. In the present paper we prove that for everyHeisenberg template an equivalent Schr\"{o}dinger template exists. We frame thequestion from a representation theory standpoint, using constructs and resultsfrom the representation theory of finite and countably infinite dimensionalvector spaces and from category theory to answer it. With the previously knownexistence of a Heisenberg template for every Schr\"{o}dinger template, ourresult establishes the equivalence of the templates.

The Equivalence of Schr\"{o}dinger and Heisenberg Pictures in Quantum Cellular Automata