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cond-mat.str-el2024★ 2 cited
A QCA for every SPT
Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings
In three dimensions, there is a nontrivial quantum cellular automaton (QCA) which disentangles the three-fermion Walker--Wang model, a model whose action depends on Stiefel--Whitne…
quant-ph2024★ 5 cited
Incompressibility and spectral gaps of random circuits
Chi-Fang Chen, Jeongwan Haah, Jonas Haferkamp +3
Random reversible and quantum circuits form random walks on the alternating group and unitary group , respectively. Known bounds on the spectr…
quant-ph2024★ 4 cited
Efficient approximate unitary designs from random Pauli rotations
Jeongwan Haah, Yunchao Liu, Xinyu Tan
We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order . Specifically, a step of the walk on the unitary or orthogn…