Phase transition of a continuous-time quantum walk on the half line

• URL: http://arxiv.org/abs/2403.13576v2
• Date: Tue, 25 Jun 2024 12:49:20 GMT
• Title: Phase transition of a continuous-time quantum walk on the half line
• Authors: Takuya Machida,
• Abstract summary: Quantum walks are referred to as quantum analogs to random walks in mathematics. We study a continuous-time quantum walk on the half line and challenge to find a limit theorem for it in this paper.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time quantum walk and the other is the continuous-time quantum walk. We study a continuous-time quantum walk on the half line and challenge to find a limit theorem for it in this paper. As a result, approximate behavior of the quantum walker is revealed after the system of quantum walk gets updated in long time.

Related papers

• On Reducing the Execution Latency of Superconducting Quantum Processors via Quantum Program Scheduling [48.142860424323395]
  We introduce the Quantum Program Scheduling Problem (QPSP) to improve the utility efficiency of quantum resources. Specifically, a quantum program scheduling method concerning the circuit width, number of measurement shots, and submission time of quantum programs is proposed to reduce the execution latency.
  arXiv  Detail & Related papers  (2024-04-11T16:12:01Z)
• Quantum walks, the discrete wave equation and Chebyshev polynomials [1.0878040851638]
  A quantum walk is the quantum analogue of a random walk. We show that quantum walks can speed up the spreading or mixing rate of random walks on graphs.
  arXiv  Detail & Related papers  (2024-02-12T17:15:19Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Quantum walks on random lattices: Diffusion, localization and the absence of parametric quantum speed-up [0.0]
  We study propagation of quantum walks on percolation-generated two-dimensional random lattices. We show that even arbitrarily weak concentrations of randomly removed lattice sites give rise to a complete breakdown of the superdiffusive quantum speed-up. The fragility of quantum speed-up implies dramatic limitations for quantum information applications of quantum walks on random geometries and graphs.
  arXiv  Detail & Related papers  (2022-10-11T10:07:52Z)
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements [3.8073142980733]
  We set up resource theories of quantum coherence and quantum entanglement for quantum measurements. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. Our results confirm that the understanding on the link between quantum coherence and quantum entanglement is valid even for quantum measurements which do not generate any quantum resource.
  arXiv  Detail & Related papers  (2022-02-25T12:24:32Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Quantum walk processes in quantum devices [55.41644538483948]
  We study how to represent quantum walk on a graph as a quantum circuit. Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
  arXiv  Detail & Related papers  (2020-12-28T18:04:16Z)
• How to Compute Using Quantum Walks [0.0]
  Quantum walks are widely and successfully used to model diverse physical processes. Quantum walks have also been shown to be universal for quantum computing. This paper explains the relationship between quantum walks as models and quantum walks as computational tools.
  arXiv  Detail & Related papers  (2020-04-03T01:51:03Z)
• Jumptime unraveling of Markovian open quantum systems [68.8204255655161]
  We introduce jumptime unraveling as a distinct description of open quantum systems. quantum jump trajectories emerge, physically, from continuous quantum measurements. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts.
  arXiv  Detail & Related papers  (2020-01-24T09:35:32Z)

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.