Fully Quantum Algorithm for the 1-dimensional linear Lattice Boltzmann Method

• URL: http://arxiv.org/abs/2606.16514v1
• Date: Mon, 15 Jun 2026 10:16:39 GMT
• Title: Fully Quantum Algorithm for the 1-dimensional linear Lattice Boltzmann Method
• Abstract summary: We present a fully quantum algorithm for solving the one-dimensional linear advection-diffusion equation using the Lattice Boltzmann method.<n>The algorithm is run on a quantum system with 133 qubits to investigate the effect of noise and the depth of the circuit on the output state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A fully quantum algorithm for solving the one-dimensional linear advection-diffusion equation using the Lattice Boltzmann method as a numerical procedure is presented in this work. We start by presenting a state of the art of the current usage of quantum algorithms for solving ordinary and partial differential equations. We then describe two algorithms for the one-dimensional Lattice Boltzmann method with two degrees of freedom. The first one is an existing hybrid quantum-classical algorithm with measurements at each time step, and the second one is our improved version, viz. a fully quantum algorithm where only one measurement is needed at the end of the algorithm. The fully quantum algorithm is first executed on a quantum simulator and then compared with a classical approach. Subsequently, the fully quantum algorithm is run on a quantum system with 133 qubits to investigate the effect of noise and the depth of the circuit on the output state. We find fluctuations in the final result due to the decoherence noise of the qubits.

Related papers

• Dynamic Circuits for the Quantum Lattice-Boltzmann Method [0.0]
  We propose a quantum algorithm for the linear advection-diffusion equation (ADE) Lattice-Boltzmann method (LBM)<n> Dynamic quantum circuits allow for an optimized collision-operator quantum algorithm, introducing partial measurements as an integral step.
  arXiv  Detail & Related papers  (2025-02-04T09:04:24Z)
• Quantum Algorithms for Stochastic Differential Equations: A Schrödingerisation Approach [29.662683446339194]
  We propose quantum algorithms for linear differential equations.<n>The gate complexity of our algorithms exhibits an $mathcalO(dlog(Nd))$ dependence on the dimensions.<n>The algorithms are numerically verified for the Ornstein-Uhlenbeck processes, Brownian motions, and one-dimensional L'evy flights.
  arXiv  Detail & Related papers  (2024-12-19T14:04:11Z)
• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states.<n>It is executable on current (hybrid) quantum hardware and does not depend on quantum memory.<n>We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• Unitary Quantum Algorithm for the Lattice-Boltzmann Method [0.0]
  We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our results demonstrate that our quantum algorithm captures non-linearity.
  arXiv  Detail & Related papers  (2024-05-22T07:03:54Z)
• The Algorithm for Solving Quantum Linear Systems of Equations With Coherent Superposition and Its Extended Applications [8.8400072344375]
  We propose two quantum algorithms for solving quantum linear systems of equations with coherent superposition. The two quantum algorithms can both compute the rank and general solution by one measurement. Our analysis indicates that the proposed algorithms are mainly suitable for conducting attacks against lightweight symmetric ciphers.
  arXiv  Detail & Related papers  (2024-05-11T03:03:14Z)
• Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck [55.22418739014892]
  We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. We apply our algorithm to the quantum information bottleneck with three quantum systems. Our numerical analysis shows that our algorithm is better than their algorithm.
  arXiv  Detail & Related papers  (2023-11-19T00:06:11Z)
• A Universal Quantum Algorithm for Weighted Maximum Cut and Ising Problems [0.0]
  We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system.
  arXiv  Detail & Related papers  (2023-06-10T23:28:13Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• Optimization and Noise Analysis of the Quantum Algorithm for Solving One-Dimensional Poisson Equation [17.65730040410185]
  We propose an efficient quantum algorithm for solving one-dimensional Poisson equation. We further develop this algorithm to make it closer to the real application on the noisy intermediate-scale quantum (NISQ) devices. We analyze the effect of common noise existing in the real quantum devices on our algorithm using the IBM Qiskit toolkit.
  arXiv  Detail & Related papers  (2021-08-27T09:44:41Z)

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.