Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond

Abstract

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by $U(1{)}_2$ Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on $2^n$-dimensional qudits that feature surface anyons described by $U(1{)}_{2^n}$ Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

arXiv comment17+8 pages, 8 figures

References in corpus (38)

• Anyons in an exactly solved model and beyond
• String-net condensation: A physical mechanism for topological phases
• Models for gapped boundaries and domain walls
• Condensate induced transitions between topologically ordered phases
• Boson topological insulators: A window into highly entangled quantum phases
• Protected edge modes without symmetry
• Fermions, strings, and gauge fields in lattice spin models
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Three-dimensional topological lattice models with surface anyons
• Index theory of one dimensional quantum walks and cellular automata
• Chiral Floquet Phases of Many-body Localized Bosons
• A review of Quantum Cellular Automata
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Generalizations and limitations of string-net models
• Commuting Pauli Hamiltonians as maps between free modules
• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• Layer construction of 3D topological states and string braiding statistics
• Dynamically enriched topological orders in driven two-dimensional systems
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Twisted foliated fracton phases
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
• Non-Abelian Hybrid Fracton Orders
• Classification of Quantum Cellular Automata
• Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
• Matrix Product Representation of Locality Preserving Unitaries
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Local Commuting Projector Hamiltonians and the Quantum Hall Effect
• Classification of Matrix-Product Unitaries with Symmetries
• An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
• Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions
• Topological lower bound on quantum chaos by entanglement growth
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Quantum cellular automata and quantum field theory in two spatial dimensions
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Effective response theory for Floquet topological systems
• An infinite family of 3d Floquet topological paramagnets
• Non-Pauli topological stabilizer codes from twisted quantum doubles

Cited by in corpus (30)

• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Nontrivial Quantum Cellular Automata in Higher Dimensions
• Pauli stabilizer models of twisted quantum doubles
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Pauli topological subsystem codes from Abelian anyon theories
• Sequential Quantum Circuits as Maps between Gapped Phases
• Higher cup products on hypercubic lattices: application to lattice models of topological phases
• Crystalline Quantum Circuits
• Learning shallow quantum circuits
• Composing topological domain walls and anyon mobility
• 3-Fermion topological quantum computation
• Invertible subalgebras
• Homological invariants of Pauli stabilizer codes
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Fundamental charges for dual-unitary circuits
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Towards topological fixed-point models beyond gappable boundaries
• Disentangling modular Walker-Wang models via fermionic invertible boundaries
• Topological phases of unitary dynamics: Classification in Clifford category
• Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Generalized Statistics on Lattices
• Fermionic defects of topological phases and logical gates
• A QCA for every SPT
• Categorifying Clifford QCA
• Topological stabilizer models on continuous variables
• Anomalies of global symmetries on the lattice
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly