Simulating discrete-time quantum walk with urn model

• URL: http://arxiv.org/abs/2506.06896v1
• Date: Sat, 07 Jun 2025 18:54:09 GMT
• Title: Simulating discrete-time quantum walk with urn model
• Authors: Surajit Saha,
• Abstract summary: Urn models have long been used to study computation processes, probability distributions, and reinforcement dynamics.<n>Meanwhile, discrete time quantum walks (DTQW) serve as fundamental components in quantum computation and quantum information theory.<n>This work explores a novel connection between an urn model and discrete-time quantum walks, focusing on how urn-based processes can provide insights into quantum state evolution and algorithmic behavior.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Urn models have long been used to study stochastic processes, probability distributions, and reinforcement dynamics. Meanwhile, discrete time quantum walks (DTQW) serve as fundamental components in quantum computation and quantum information theory. This work explores a novel connection between an urn model and discrete-time quantum walks, focusing on how urn-based stochastic processes can provide insights into quantum state evolution and algorithmic behavior. Importantly, our model operates entirely with real-valued quantities, without relying on complex amplitudes of the quantum walk. Every stochastic rule is derived from urn-based processes, whose parameters are governed by the coin and shift mechanisms of the quantum walk, maintaining the structural dynamics of the DTQW. Through this interdisciplinary approach, we aim to bridge classical and quantum frameworks, offering new perspectives on both quantum algorithms and stochastic modeling. This work connects the urn model to the broad range of applications where DTQWs are successfully employed.

Related papers

• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [60.996803677584424]
  Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning.<n>Their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise.<n>This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Quantum Simulation for Dynamical Transition Rates in Open Quantum Systems [0.0]
  We introduce a novel and efficient quantum simulation method to compute dynamical transition rates in Markovian open quantum systems.<n>Our new approach holds the potential to surpass the bottlenecks of current quantum chemical research.
  arXiv  Detail & Related papers  (2024-12-23T02:53:05Z)
• Neural Quantum Propagators for Driven-Dissipative Quantum Dynamics [0.0]
  We develop driven neural quantum propagators (NQP), a universal neural network framework that solves driven-dissipative quantum dynamics. NQP can handle arbitrary initial quantum states, adapt to various external fields, and simulate long-time dynamics, even when trained on far shorter time windows. We demonstrate the effectiveness of our approach by studying the spin-boson and the three-state transition Gamma models.
  arXiv  Detail & Related papers  (2024-10-21T15:13:17Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• A new quantum machine learning algorithm: split hidden quantum Markov model inspired by quantum conditional master equation [14.262911696419934]
  We introduce the split HQMM (SHQMM) for implementing the hidden quantum Markov process. Experimental results suggest our model outperforms previous models in terms of scope of applications and robustness.
  arXiv  Detail & Related papers  (2023-07-17T16:55:26Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Floquet engineering of continuous-time quantum walks: towards the simulation of complex and next-to-nearest neighbor couplings [0.0]
  We apply the idea of Floquet engineering in the context of continuous-time quantum walks on graphs. We define periodically-driven Hamiltonians which can be used to simulate the dynamics of certain target quantum walks. Our work provides explicit simulation protocols that may be used for directing quantum transport, engineering the dispersion relation of one-dimensional quantum walks or investigating quantum dynamics in highly connected structures.
  arXiv  Detail & Related papers  (2020-12-01T12:46:56Z)
• Expressibility and trainability of parameterized analog quantum systems for machine learning applications [0.0]
  We show how interplay between external driving and disorder in the system dictates the trainability and expressibility of interacting quantum systems. Our work shows the fundamental connection between quantum many-body physics and its application in machine learning.
  arXiv  Detail & Related papers  (2020-05-22T14:59:42Z)
• Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer [1.2324860823895265]
  We present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.
  arXiv  Detail & Related papers  (2020-02-06T22:24:56Z)

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.