Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits

• URL: http://arxiv.org/abs/2108.07235v3
• Date: Mon, 21 Nov 2022 16:49:30 GMT
• Title: Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
• Authors: Marko J. Ran\v{c}i\'c
• Abstract summary: Majorana-zero-modes were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Majorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs-the result reproducibility crisis.

Related papers

• Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice [0.0]
  We simulate the non-Abelian exchange of Majorana zero modes (MZMs) on a quantum computer. We detail the protocol for braiding two and four MZMs in terms of a spin Hamiltonian.
  arXiv  Detail & Related papers  (2025-03-19T16:45:19Z)
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States [39.58317527488534]
  We investigate the impact of introducing a local cavity within the center of a topological chain. This cavity induces a scissor-like effect that bisects the chain, liberating Majorana zero modes (MZMs) within the bulk. By leveraging the symmetry properties of fermion modes within a two-site cavity, we propose a novel method for generating MZM-polariton Schr"odinger cat states.
  arXiv  Detail & Related papers  (2024-09-06T18:00:00Z)
• Stability of Majorana zero modes with quantum optical lattices [0.0]
  I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. MZM have potential applications for quantum information as they are topologically protected analogous to the behaviour of the Kitaev chain.
  arXiv  Detail & Related papers  (2024-08-16T06:44:20Z)
• Majorana zero-modes in a dissipative Rashba nanowire [0.0]
  We study the impact of dissipation on a superconducting Rashba nanowire. We reveal that the system can still host Majorana zero-modes (MZMs) with a finite lifetime in the presence of dissipation.
  arXiv  Detail & Related papers  (2024-03-01T10:13:54Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers [49.1574468325115]
  We introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.
  arXiv  Detail & Related papers  (2023-05-30T18:00:05Z)
• Informationally complete measures of quantum entanglement [0.0]
  We introduce a family of entanglement measures which are given by the complete eigenvalues of the reduced density matrices of the system. It is demonstrated that such ICEMs can characterize finer and distinguish better the entanglement than existing well-known entanglement measures.
  arXiv  Detail & Related papers  (2022-06-22T19:27:07Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences [0.0]
  We show the usefulness of multiple quantum coherences for probing equilibrium phase transitions in non-Hermitian systems. Our results have applications to non-Hermitian quantum sensing, quantum thermodynamics, and in the study of the non-Hermitian skin effect.
  arXiv  Detail & Related papers  (2021-09-06T14:30:47Z)
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices [69.50862982117127]
  We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
  arXiv  Detail & Related papers  (2020-11-28T11:23:06Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.