Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number

• URL: http://arxiv.org/abs/2310.17973v4
• Date: Tue, 9 Jan 2024 15:17:22 GMT
• Title: Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
• Authors: Claudio Sanavio and Sauro Succi
• Abstract summary: We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method. We show that, at least for moderate Reynolds numbers between 10 and 100, the Carleman-LB procedure can be successfully truncated at second order.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method. First, we demonstrate the convergence of the classical Carleman procedure at moderate Reynolds numbers, namely for Kolmogorov-like flows. Then we proceed to formulate the corresponding quantum algorithm, including the quantum circuit layout and analyze its computational viability. We show that, at least for moderate Reynolds numbers between 10 and 100, the Carleman-LB procedure can be successfully truncated at second order, which is a very encouraging result. We also show that the quantum circuit implementing the single time-step collision operator has a fixed depth, regardless of the number of lattice sites. However, such depth is of the order of ten thousands quantum gates, meaning that quantum advantage over classical computing is not attainable today, but could be achieved in the near-mid term future. The same goal for the multi-step version remains however an open topic for future research.

Related papers

• Carleman-lattice-Boltzmann quantum circuit with matrix access oracles [0.0]
  We apply Carleman linearization of the Lattice Boltzmann representation of fluid flows to quantum emulate the dynamics of a 2D Kolmogorov-like flow. We first define a gate-based quantum circuit for the implementation of the CLB method and then exploit the sparse nature of the CLB matrix to build a quantum circuit based on block-encoding techniques.
  arXiv  Detail & Related papers  (2025-01-05T15:32:14Z)
• On the practicality of quantum sieving algorithms for the shortest vector problem [42.70026220176376]
  lattice-based cryptography is one of the main candidates of post-quantum cryptography. cryptographic security against quantum attackers is based on lattice problems like the shortest vector problem (SVP) Asymptotic quantum speedups for solving SVP are known and rely on Grover's search.
  arXiv  Detail & Related papers  (2024-10-17T16:54:41Z)
• Carleman-Grad approach to the quantum simulation of fluids [0.0]
  We show that the Carleman-Grad procedure exhibits intermediate properties between the two. Namely, convergence of the Carleman iteration over a few tens of timesteps and a potentially viable quantum circuit implementation using quantum linear algebra solvers.
  arXiv  Detail & Related papers  (2024-06-03T08:58:40Z)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method [39.671915199737846]
  We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations. The presented method is validated and demonstrated for 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• On the importance of data encoding in quantum Boltzmann methods [0.0]
  We show that for encodings commonly discussed in literature either the collision or the streaming step cannot be unitary. We propose a novel encoding in which the number of qubits used to encode the velocity depends on the number of time steps one wishes to simulate. Our encoding method is to the best of our knowledge the only one currently known that can be used for a start-to-end quantum Boltzmann solver.
  arXiv  Detail & Related papers  (2023-02-10T15:05:33Z)
• Quantum Speedup for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection [2.5272389610447856]
  We propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization problem. The proposed algorithm is capable of reducing the query complexity in the classical domain and providing a quadratic speedup in the quantum domain.
  arXiv  Detail & Related papers  (2022-05-31T00:14:49Z)
• 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)
• Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits [63.83649593474856]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Fast Swapping in a Quantum Multiplier Modelled as a Queuing Network [64.1951227380212]
  We propose that quantum circuits can be modeled as queuing networks. Our method is scalable and has the potential speed and precision necessary for large scale quantum circuit compilation.
  arXiv  Detail & Related papers  (2021-06-26T10:55:52Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)

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.