Three-dimensional chiral quantum cellular automata previously considered simple copies of Witt groups now defy all attempts at efficient simulation via standard quantum circuits. This work demonstrates these specific automata are fundamentally more complex than once believed, remaining intractable even when expanded with ancillary degrees of freedom or translated in space. For every odd prime p, this research establishes I(Bp,k) = [p], revealing an unexpected structure within their underlying group properties.
Researchers Find Complex Automata Aren’t Standard Circuits
Three-dimensional chiral quantum cellular automata previously considered simple copies of Witt groups now defy all attempts at efficient simulation via standard quantum circuits. This work demonstrates these specific automata are fundamentally more complex than once believed, remaining intractable even when expanded with ancillary degrees of freedom or translated in space. For every odd prime *p*, this research establishes I(Bp,k) = [p], revealing an unexpected structure within their underlyi...