Short remarks on shallow unitary circuits

2025/04/18 by Haah, Jeongwan · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2504.14005

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.

Cited by

• Random unitaries from Hamiltonian dynamics
• Generative quantum advantage for classical and quantum problems

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