Non-onsite symmetries and quantum teleportation in split-index matrix product states
arXiv:2404.15883 · doi:10.22331/q-2025-05-12-1738
Abstract
We describe a class of spin chains with new physical and computational properties. On the physical side, the spin chains give examples of symmetry-protected topological phases that are defined by non-onsite symmetries, i.e. symmetries that are not a tensor product of single-site operators. These phases can be detected by string-order parameters, but notably do not exhibit entanglement spectrum degeneracy. On the computational side, the spin chains represent a new class of states that can be used to deterministically teleport information across long distances, with the novel property that the necessary classical side processing is a non-linear function of the measurement outcomes. We also give examples of states that can serve as universal resources for measurement-based quantum computation, providing the first examples of such resources without entanglement spectrum degeneracy. The key tool in our analysis is a new kind of tensor network representation which we call split-index matrix product states (SIMPS). We develop the basic formalism of SIMPS, compare them to matrix product states, show how they are better equipped to describe certain kinds of non-onsite symmetries including anomalous symmetries, and discuss how they are also well-suited to describing quantum teleportation and constrained spin chains.
arXiv commentv4: Published version. v2: Extended discussion on anomalous symmetries
References in corpus (70)
- The density-matrix renormalization group in the age of matrix product states
- Probing many-body dynamics on a 51-atom quantum simulator
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Persistent entanglement in arrays of interacting particles
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Measurement-based quantum computation with cluster states
- Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
- Entanglement spectrum of a topological phase in one dimension
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- Symmetry protection of topological order in one-dimensional quantum spin systems
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Classifying quantum phases using Matrix Product States and PEPS
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Entanglement versus Correlations in Spin Systems
- 2D symmetry protected topological orders and their protected gapless edge excitations
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
- Detection of Symmetry Protected Topological Phases in 1D
- Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
- Entanglement spectrum and boundary theories with projected entangled-pair states
- PEPS as ground states: degeneracy and topology
- String order and symmetries in quantum spin lattices
- Novel schemes for measurement-based quantum computation
- Contextuality in Measurement-based Quantum Computation
- Localizable Entanglement
- Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
- Symmetry-protected phases for measurement-based quantum computation
- Quantum phase transitions in matrix product systems
- Quantum computation on the edge of a symmetry-protected topological order
- Identifying phases of quantum many-body systems that are universal for quantum computation
- Identification of symmetry-protected topological states on noisy quantum computers
- Long-range entanglement from measuring symmetry-protected topological phases
- Slow quantum thermalization and many-body revivals from mixed phase space
- A computationally universal phase of quantum matter
- Hierarchy of universal entanglement in 2D measurement-based quantum computation
- Computational Power of Symmetry-Protected Topological Phases
- Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
- Topological order in 1D Cluster state protected by symmetry
- Universal quantum computation using fractal symmetry-protected cluster phases
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
- Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
- Resource quality of a symmetry-protected topologically ordered phase for quantum computation
- Quantum circuit complexity of one-dimensional topological phases
- The hidden symmetry-breaking picture of symmetry-protected topological order
- Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
- Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
- The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
- Classifying phases protected by matrix product operator symmetries using matrix product states
- Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
- A generalization of the injectivity condition for Projected Entangled Pair States
- Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
- Normal projected entangled pair states generating the same state
- Type-II fractons from coupled spin chains and layers
- Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
- Symmetry-Protected Topological Entanglement
- Optimal steering of matrix product states and quantum many-body scars
- Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
- Detecting subsystem symmetry protected topological order via entanglement entropy
- Boson condensation and instability in the tensor network representation of string-net states
- Matrix Product States with Backflow correlations
- Inaccessible entanglement in symmetry protected topological phases
- Matrix Product States with long-range Localizable Entanglement
- Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
- Quantum teleportation implies symmetry-protected topological order
- Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices