Year: 2025
Type: article
Abstract: (i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the case with a continuous onsite symmetry or with a local energy conservation law. (ii) We explain a simple algorithm for a formulation of the shallow unitary circuit learning problem and relate it to an open question on strictly locality-preserving unitaries (quantum cellular automata). (iii) We show that any translation-invariant quantum cellular automaton in D -dimensional lattice of volume V can be implemented using only O ( V ) local gates in a staircase fashion using invertible subalgebra pumping.
Source: Quantum
Author: Jeongwan Haah
Institutions: Google (United States), Stanford University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
OpenAlex ID: W4417245470