A QCA for every SPT

Abstract

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--Whitney classes of the spacetime manifold. Here we present a conjectured generalization to higher dimensions. For an arbitrary symmetry protected topological phase of time reversal whose action depends on Stiefel--Whitney classes, we construct a corresponding QCA that we conjecture disentangles that phase. Some of our QCA are Clifford, and we relate these to a classification theorem of Clifford QCA. We identify Clifford QCA in $4m+1$ dimensions, for which we find a low-depth circuit description using non-Clifford gates but not with Clifford gates.

v2, corrects and clarifies the Stiefel Whitney - QCA correspondence

References in corpus (18)

• Anyons in an exactly solved model and beyond
• Index theory of one dimensional quantum walks and cellular automata
• Chiral Floquet Phases of Many-body Localized Bosons
• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• Interacting invariants for Floquet phases of fermions in two dimensions
• Bosonization in three spatial dimensions and a 2-form gauge theory
• Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d
• Classification of Quantum Cellular Automata
• Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
• Exact bosonization in arbitrary dimensions
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Higher cup products on hypercubic lattices: application to lattice models of topological phases
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
• Gravitational anomaly of 3+1 dimensional Z_2 toric code with fermionic charges and fermionic loop self-statistics
• Quantum cellular automata and quantum field theory in two spatial dimensions
• 3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems
• Topological phases of unitary dynamics: Classification in Clifford category