Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
arXiv:2405.15853 · doi:10.21468/SciPostPhys.17.4.113
Abstract
Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.
76 pages, 13 figures, published version
References in corpus (40)
- Local stabilizer codes in three dimensions without string logical operators
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Higher Gauging and Non-invertible Condensation Defects
- Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
- Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
- Dynamically Generated Logical Qubits
- Measurement as a shortcut to long-range entangled quantum matter
- Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
- Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
- Topological Defects on the Lattice: Dualities and Degeneracies
- Foliated Quantum Codes
- Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
- Long-range entanglement from measuring symmetry-protected topological phases
- Homological Error Correction: Classical and Quantum Codes
- Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
- Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
- Floquet codes without parent subsystem codes
- Anomaly Inflow for Subsystem Symmetries
- Anyon condensation and the color code
- What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
- Subsystem Non-Invertible Symmetry Operators and Defects
- High-threshold quantum computing by fusing one-dimensional cluster states
- Topological symmetry in quantum field theory
- Introduction to Generalized Global Symmetries in QFT and Particle Physics
- Sequential Quantum Circuits as Maps between Gapped Phases
- Probing sign structure using measurement-induced entanglement
- Efficiently preparing Schrödinger's cat, fractons and non-Abelian topological order in quantum devices
- Measurement-Based Quantum Computation
- Decoding Measurement-Prepared Quantum Phases and Transitions: from Ising model to gauge theory, and beyond
- Quantum spin systems for measurement-based quantum computation
- Foliated BF theories and Multipole symmetries
- Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
- Adaptive constant-depth circuits for manipulating non-abelian anyons
- Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
- Multipole and fracton topological order via gauging foliated SPT phases
- Universal structure of measurement-induced information in many-body ground states
- Measurement-based quantum simulation of Abelian lattice gauge theories
- Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
- CFT from TQFT via Holographic Tensor Network, and Precision Discretisation of CFT
- The Physics of (good) LDPC Codes II. Product constructions