Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space

• URL: http://arxiv.org/abs/2311.18497v2
• Date: Thu, 20 Jun 2024 22:51:01 GMT
• Title: Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space
• Authors: Shang Liu,
• Abstract summary: We show that ground states of all quantum double models can be efficiently prepared in the doubled Hilbert space. Nontrivial anyon braiding effects, both abelian and nonabelian, can be realized in the doubled Hilbert space.
• Score: 4.097395387450313
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Realizing nonabelian topological orders and their anyon excitations is an esteemed objective. In this work, we propose a novel approach towards this goal: quantum simulating topological orders in the doubled Hilbert space - the space of density matrices. We show that ground states of all quantum double models (toric code being the simplest example) can be efficiently prepared in the doubled Hilbert space; only finite-depth local operations are needed. In contrast, this is not the case in the conventional Hilbert space: Ground states of only some of these models are known to be efficiently preparable. Additionally, we find that nontrivial anyon braiding effects, both abelian and nonabelian, can be realized in the doubled Hilbert space, although the intrinsic nature of density matrices restricts possible excitations.

Related papers

• Towards entropic uncertainty relations for non-regular Hilbert spaces [44.99833362998488]
  The Entropic Uncertainty Relations (EUR) result from inequalities that are intrinsic to the Hilbert space and its dual with no direct connection to the Canonical Commutation Relations. The analysis of these EUR in the context of singular Hilbert spaces has not been addressed.
  arXiv  Detail & Related papers  (2025-03-24T23:41:50Z)
• Local unambiguous unidentifiability, entanglement generation, and Hilbert space splitting [0.0]
  We consider collections of mixed states supported on mutually orthogonal subspaces whose rank add up to the total dimension of the underlying Hilbert space. No state from the set can be unambiguously identified by local operations and classical communication (LOCC) with non-zero success probability. We show the necessary and sufficient condition for such a property to exist is that the states must be supported in entangled subspaces.
  arXiv  Detail & Related papers  (2025-03-07T18:33:19Z)
• Non-Orientable Quantum Hilbert Space Bundle [0.0]
  Instead of relying on hints from the Hamiltonian eigenvalues, the behavior of the fiber metric and the evolution of quantum states are analyzed. The results reveal that the Hilbert space bundle around an exceptional point is non-orientable.
  arXiv  Detail & Related papers  (2024-12-09T14:58:26Z)
• Quantum Simulation of Large N Lattice Gauge Theories [0.0]
  A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of QCD. We show how the Hilbert space and interactions can be expanded in inverse powers of $N_c$.
  arXiv  Detail & Related papers  (2024-11-14T17:43:50Z)
• Kernel Operator-Theoretic Bayesian Filter for Nonlinear Dynamical Systems [25.922732994397485]
  We propose a machine-learning alternative based on a functional Bayesian perspective for operator-theoretic modeling. This formulation is directly done in an infinite-dimensional space of linear operators or Hilbert space with universal approximation property. We demonstrate that this practical approach can obtain accurate results and outperform finite-dimensional Koopman decomposition.
  arXiv  Detail & Related papers  (2024-10-31T20:31:31Z)
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space [0.0]
  We show that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using a simplified subset of eligible metrics and two exactly solvable models.
  arXiv  Detail & Related papers  (2024-08-05T14:14:51Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Constraint Inequalities from Hilbert Space Geometry & Efficient Quantum Computation [0.0]
  Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. We describe the procedure and point out that this parallels the necessary considerations that make Quantum Simulation of quantum fields possible. We suggest how to use these ideas to guide and improve parameterized quantum circuits.
  arXiv  Detail & Related papers  (2022-10-13T22:13:43Z)
• Universality of a truncated sigma-model [0.0]
  Even when regularized using a finite lattice, Bosonic quantum field theories possess an infinite dimensional Hilbert space. A qubitization of the $1+1$ dimensionalally free $sigma$-model based on ideas of non-commutative geometry was previously proposed. We provide evidence that it reproduces the physics of the $sigma$-model both in the infrared and the ultraviolet regimes.
  arXiv  Detail & Related papers  (2021-09-15T18:06:07Z)
• Qubit regularization of asymptotic freedom [35.37983668316551]
  Heisenberg-comb acts on a Hilbert space with only two qubits per spatial lattice site. We show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units. We argue that near-term quantum computers may suffice to demonstrate freedom.
  arXiv  Detail & Related papers  (2020-12-03T18:41:07Z)
• Quantum Space, Quantum Time, and Relativistic Quantum Mechanics [0.0]
  We treat space and time as quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order translations Hamiltonian and momentum constraints.
  arXiv  Detail & Related papers  (2020-04-20T09:04:15Z)

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.