Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation

• URL: http://arxiv.org/abs/2310.10561v3
• Date: Fri, 5 Jan 2024 21:40:31 GMT
• Title: Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation
• Authors: Zhuohao Liu, Emma C. Johnson, and David L. Feder
• Abstract summary: All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order. This work considers two families of one-dimensional qubit states to answer this question in the negative.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-onsite symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry.

Related papers

• Critical Fermions are Universal Embezzlers [44.99833362998488]
  We show that universal embezzlers are ubiquitous in many-body physics. The same property holds in locally-interacting, dual spin chains via the Jordan-Wigner transformation.
  arXiv  Detail & Related papers  (2024-06-17T17:03:41Z)
• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• 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)
• Redundant String Symmetry-Based Error Correction: Experiments on Quantum Devices [0.0]
  Computational power in measurement-based quantum computing stems from symmetry protected topological (SPT) order of the entangled resource state. We introduce a quantum error correction (QEC) approach using redundant non-local symmetry of the resource state. We identify the underlying redundant-SPT order as error-protected degeneracies in the entanglement spectrum.
  arXiv  Detail & Related papers  (2023-10-19T16:05:43Z)
• The distinctive symmetry of Bell states [65.268245109828]
  The Bell's basis is composed of four maximally entangled states of two qubits. The aim of this paper is to find out the symmetries that determine a Bell state.
  arXiv  Detail & Related papers  (2023-08-14T17:02:41Z)
• Is there a finite complete set of monotones in any quantum resource theory? [39.58317527488534]
  We show that there does not exist a finite set of resource monotones which completely determines all state transformations. We show that totally ordered theories allow for free transformations between all pure states.
  arXiv  Detail & Related papers  (2022-12-05T18:28:36Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Time-space duality in 2D quantum gravity [0.0]
  We show that any two points are equally probable to be timelike and spacelike separated in a universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present.
  arXiv  Detail & Related papers  (2021-09-20T15:45:48Z)
• Entangling power of symmetric two-qubit quantum gates [0.0]
  capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. We focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space. A geometric description of the local equivalence classes of gates is given in terms of the $mathfraksu(3)$ Lie algebra root vectors.
  arXiv  Detail & Related papers  (2021-07-27T08:06:32Z)
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps [0.0]
  We show that it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with feedforward correction is sufficient to recover a cluster-like state.
  arXiv  Detail & Related papers  (2021-07-08T17:56:19Z)
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality [0.6882042556551611]
  We study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors. We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures. We report a relation between quantum coherence and path complementary distinguishability in a double-slit set-up.
  arXiv  Detail & Related papers  (2020-05-17T16:56:31Z)

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.