Non-onsite symmetries and quantum teleportation in split-index matrix product states
- URL: http://arxiv.org/abs/2404.15883v1
- Date: Wed, 24 Apr 2024 14:04:10 GMT
- Title: Non-onsite symmetries and quantum teleportation in split-index matrix product states
- Authors: David T. Stephen,
- Abstract summary: 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.
On the computational side, the spin chains represent a new class of states that can be used to deterministically teleport information across long distances.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 and quantum teleportation, and discuss how they are also well-suited to describing constrained spin chains.
Related papers
- Quantum Algorithms for Realizing Symmetric, Asymmetric, and Antisymmetric Projectors [3.481985817302898]
Knowing the symmetries of a given system or state obeys or disobeys is often useful in quantum computing.
We present a collection of quantum algorithms that realize projections onto the symmetric subspace.
We show how projectors can be combined in a systematic way to effectively measure various projections in a single quantum circuit.
arXiv Detail & Related papers (2024-07-24T18:00:07Z) - Non-invertible symmetries act locally by quantum operations [0.552480439325792]
Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries.
Non-invertible symmetries act on local operators by quantum operations.
arXiv Detail & Related papers (2024-03-29T08:54:53Z) - Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$.
It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
arXiv Detail & Related papers (2024-02-26T06:23:39Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras
from First Principles [55.41644538483948]
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset.
We use fully connected neural networks to model the transformations symmetry and the corresponding generators.
Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
arXiv Detail & Related papers (2023-01-13T16:25:25Z) - Symmetries and field tensor network states [0.6299766708197883]
We study the interplay between symmetry representations of the physical and virtual space on the class of tensor network states for critical spins systems.
We can represent a symmetry on the physical index as a commutator with the corresponding CFT current on the virtual space.
We derive the critical symmetry protected topological properties of the two ground states of the Majumdar-Ghosh point with respect to the previously defined symmetries.
arXiv Detail & Related papers (2022-09-22T18:01:39Z) - Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
We show how classical probability theory can be extended to include any system with incompatible variables.
We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
arXiv Detail & Related papers (2022-05-31T16:04:59Z) - Symmetry protected entanglement in random mixed states [0.0]
We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space.
In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
arXiv Detail & Related papers (2021-11-30T19:00:07Z) - Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity.
This enables an exact description of the full dynamics and dissipative spectrum.
Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
arXiv Detail & Related papers (2021-09-27T17:45:42Z) - Symmetry Breaking in Symmetric Tensor Decomposition [44.181747424363245]
We consider the nonsymmetry problem associated with computing the points rank decomposition of symmetric tensors.
We show that critical points the loss function is detected by standard methods.
arXiv Detail & Related papers (2021-03-10T18:11:22Z) - Detecting Symmetries with Neural Networks [0.0]
We make extensive use of the structure in the embedding layer of the neural network.
We identify whether a symmetry is present and to identify orbits of the symmetry in the input.
For this example we present a novel data representation in terms of graphs.
arXiv Detail & Related papers (2020-03-30T17:58:24Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.