Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function

• URL: http://arxiv.org/abs/2304.13235v2
• Date: Sun, 16 Jun 2024 18:53:56 GMT
• Title: Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Authors: Shang Liu,
• Abstract summary: topological entanglement entropy can be used to detect nontrivial topological order from a ground state wave function. We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. This protocol is validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.
• Score: 4.097395387450313
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Realizing topological orders and topological quantum computation is a central task of modern physics. An important but notoriously hard question in this endeavor is how to diagnose topological orders that lack conventional order parameters. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to detect nontrivial topological order from a ground state wave function, but is far from enough for fully determining the topological order. In this work, we take a key step further in this direction: We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. The choice of the space manifold and the ground state is arbitrary. This protocol is both validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.

Related papers

• Probing topological entanglement on large scales [0.0]
  Topologically ordered quantum matter exhibits intriguing long-range patterns of entanglement, which reveal themselves in subsystem entropies. We propose a protocol based on local adiabatic deformations of the Hamiltonian which extracts the universal features of long-range entanglement.
  arXiv  Detail & Related papers  (2024-08-22T18:00:01Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer [0.0]
  We show for the first time a constant-depth procedure for creating a toric code ground state in real-time. We create a non-Abelian defect whose presence is confirmed by transmuting anyons via braiding. This work clears the way towards creating complex topological orders in the lab.
  arXiv  Detail & Related papers  (2023-02-03T18:50:57Z)
• Topological Quantum Programming in TED-K [0.0]
  We describe a fundamental and natural scheme that we are developing, for typed functional (hence verifiable) topological quantum programming. It reflects the universal fine technical detail of topological q-bits, namely of symmetry-protected (or enhanced) topologically ordered Laughlin-type anyon ground states. The language system is under development at the "Center for Quantum and Topological Systems" at the Research Institute of NYU, Abu Dhabi.
  arXiv  Detail & Related papers  (2022-09-17T14:00:37Z)
• Quantum Field Theories, Topological Materials, and Topological Quantum Computing [3.553493344868414]
  A quantum computer can perform exponentially faster than its classical counterpart. Topology and knot theory, geometric phases, topological materials, topological quantum field theories, recoupling theory, and category theory are discussed.
  arXiv  Detail & Related papers  (2022-08-20T15:12:44Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Probing Topological Spin Liquids on a Programmable Quantum Simulator [40.96261204117952]
  We use a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms are placed on the links of a kagome lattice and evolution under Rydberg blockade creates frustrated quantum states. The onset of a quantum spin liquid phase of the paradigmatic toric code type is detected by evaluating topological string operators.
  arXiv  Detail & Related papers  (2021-04-09T00:18:12Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Quantum Hall phase emerging in an array of atoms interacting with photons [101.18253437732933]
  Topological quantum phases underpin many concepts of modern physics. Here, we reveal that the quantum Hall phase with topological edge states, spectral Landau levels and Hofstadter butterfly can emerge in a simple quantum system. Such systems, arrays of two-level atoms (qubits) coupled to light being described by the classical Dicke model, have recently been realized in experiments with cold atoms and superconducting qubits.
  arXiv  Detail & Related papers  (2020-03-18T14:56:39Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.