Quantum computing of fluid dynamics using the hydrodynamic Schr\"odinger equation

• URL: http://arxiv.org/abs/2302.09741v1
• Date: Mon, 20 Feb 2023 03:43:27 GMT
• Title: Quantum computing of fluid dynamics using the hydrodynamic Schr\"odinger equation
• Authors: Zhaoyuan Meng and Yue Yang
• Abstract summary: We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schr"odinger equation (HSE) We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with exponential speedup.
• Score: 7.752417113600681
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schr\"odinger equation (HSE), which can be promising in simulating three-dimensional turbulent flows in various engineering applications. The HSE is derived by generalizing the Madelung transform to compressible/incompressible flows with finite vorticity and dissipation. Since the HSE is expressed as a unitary operator on a two-component wave function, it is more suitable than the NSE for quantum computing. The flow governed by the HSE can resemble a turbulent flow consisting of tangled vortex tubes with the five-thirds scaling of energy spectrum. We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with exponential speedup.

Related papers

• Simulating unsteady fluid flows on a superconducting quantum processor [23.24560103938476]
  We report an experiment on the digital simulation of unsteady flows, which consists of quantum encoding, evolution, and detection of flow states. This work demonstrates the potential of quantum computing in simulating more complex flows, such as turbulence, for practical applications.
  arXiv  Detail & Related papers  (2024-04-24T13:45:43Z)
• Quantum computing of reacting flows via Hamiltonian simulation [13.377719901871027]
  We develop the quantum spectral and finite difference methods for simulating reacting flows in periodic and general conditions. The present quantum computing algorithms offer a one-shot'' solution for a given time without temporal discretization.
  arXiv  Detail & Related papers  (2023-12-13T04:31:49Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Ensemble Fluid Simulations on Quantum Computers [0.0]
  We discuss the viability of ensemble simulations of fluid flows on quantum computers. We formulate a functional Liouville equation for the probability distribution of the flow field configuration. After suitable marginalization and closure, the Liouville approach is shown to require several hundreds of logical qubits.
  arXiv  Detail & Related papers  (2023-04-11T16:51:02Z)
• Potential quantum advantage for simulation of fluid dynamics [1.4046104514367475]
  We show that a potential quantum exponential speedup can be achieved to simulate the Navier-Stokes equations governing turbulence using quantum computing. This work suggests that an exponential quantum advantage may exist for simulating nonlinear multiscale transport phenomena.
  arXiv  Detail & Related papers  (2023-03-29T09:14:55Z)
• Verifiably Exact Solution of the Electronic Schr\"odinger Equation on Quantum Devices [0.0]
  We present an algorithm that yields verifiably exact solutions of the many-electron Schr"odinger equation. We demonstrate the algorithm on both quantum simulators and noisy quantum computers.
  arXiv  Detail & Related papers  (2023-03-01T19:00:00Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Implementation of a two-stroke quantum heat engine with a collisional model [50.591267188664666]
  We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBMQ processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm.
  arXiv  Detail & Related papers  (2022-03-25T16:55:08Z)
• 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)
• Probing quantum information propagation with out-of-time-ordered correlators [41.12790913835594]
  Small-scale quantum information processors hold the promise to efficiently emulate many-body quantum systems. Here, we demonstrate the measurement of out-of-time-ordered correlators (OTOCs) A central requirement for our experiments is the ability to coherently reverse time evolution.
  arXiv  Detail & Related papers  (2021-02-23T15:29:08Z)
• 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)

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.