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arXiv:2312.01664 · Physical Review Applied

Quantum algorithm for the radiative-transfer equation

Asuka Igarashi, Tadashi Kadowaki, Shiro Kawabata

Published Mar 7, 2024• 3 citations
arXivHTMLPDF

Abstract

The radiation transfer equation is widely used for simulations, for example, heat transfer in engineering, diffuse optical tomography in healthcare, and radiation hydrodynamics in astrophysics. By combining the lattice Boltzmann method, we propose a quantum algorithm for radiative transfer. This algorithm encompasses all the essential physical processes of radiative transfer: absorption, scattering, and emission. Although a sufficient number of measurements are required to precisely estimate the quantum state, and the initial encoding of the quantum state remains a challenging problem, our quantum algorithm exponentially accelerates radiative-transfer calculations compared to classical algorithms. In order to verify the quantum algorithm, we perform quantum circuit simulation using IBM Qiskit Aer and find good agreement between our numerical result and the exact solution. The algorithm paves the way for applications, such as fault-tolerant quantum computers for plasma engineering, telecommunications, nuclear-fusion technology, healthcare, and astrophysics. Published by the American Physical Society 2024

DOI
10.1103/physrevapplied.21.034010

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The radiation transfer equation is widely used for simulations, for example, heat transfer in engineering, diffuse optical tomography in healthcare, and radiation hydrodynamics in astrophysics. By combining the lattice Boltzmann method, we propose a quantum algorithm for radiative transfer. This algorithm encompasses all the essential physical processes of radiative transfer: absorption, scattering, and emission. Although a sufficient number of measurements are required to precisely estimate the quantum state, and the initial encoding of the quantum state remains a challenging problem, our quantum algorithm exponentially accelerates radiative-transfer calculations compared to classical algorithms. In order to verify the quantum algorithm, we perform quantum circuit simulation using IBM Qiskit Aer and find good agreement between our numerical result and the exact solution. The algorithm paves the way for applications, such as fault-tolerant quantum computers for plasma engineering, telecommunications, nuclear-fusion technology, healthcare, and astrophysics. Published by the American Physical Society 2024
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We present a versatile and efficient quantum algorithm based on the Lattice Boltzmann method (LBM) approximate solution of the linear advection-diffusion equation (ADE). We emphasize that the LBM approximation modifies the diffusion term of the underlying exact ADE and leads to a modified equation (mADE). Due to its versatility in terms of operator splitting, the proposed quantum LBM algorithm for the mADE provides a building block for future quantum algorithms to solve the linearized Navier-Stokes equation on quantum computers. We split the algorithm into four operations: initialization, collision, streaming, and calculation of the macroscopic quantities. We propose general quantum building blocks for each operator, which adapt intrinsically from the general three-dimensional case to smaller dimensions and apply to arbitrary lattice-velocity sets. Based on (sub-linear) amplitude data encoding, we propose improved initialization and collision operations with reduced complexity and efficient sampling-based simulation. Quantum streaming algorithms are based on previous developments. The proposed quantum algorithm allows for the computation of successive time steps, requiring full state measurement and reinitialization after every time step. It is validated by comparison with a digital implementation and based on analytical solutions in one and two dimensions. Furthermore, we demonstrate the versatility of the quantum algorithm for two cases with non-uniform advection velocities in two and three dimensions. Various velocity sets are considered to further highlight the flexibility of the algorithm. We benchmark our optimized quantum algorithm against previous methods employed in sampling-based quantum simulators. We demonstrate sampling efficiency, with sampling accelerated convergence requiring fewer shots. • Novel LBM quantum algorithm for solving the linear advection-diffusion equation with variable velocity as a building block. • Modular quantum algorithm for 1 through 3 spatial dimensions and all common lattice-velocity sets. • Significant reduction in quantum-algorithm complexity achieved through efficient encoding strategy leveraging symmetries. • Improved collision quantum-algorithm building block leading to higher success rates for the collision operator. • Benchmarking shows faster convergence and reduced shot requirements compared to previous algorithms.