Feasibility study to quantify the potential of using quantum algorithms to simulate MHD effects in liquid metals

这项工作解决了模拟液态金属如Li或LiPb的磁流体动力学方程的计算挑战，这些液态金属被用作核聚变反应堆中中子倍增器和氚增殖的冷却剂和源。该项目是对使用量子算法模拟液态金属磁流体动力学的可行性研究，液态金属在核聚变反应堆中用作冷却剂和氚来源。聚变工业需要对高强度磁场下液态金属动力学的准确预测，由于存在磁场引起的湍流等现象，模拟聚变反应堆内的液态金属流动面临一些特殊的挑战。就聚变反应堆中的氚增殖而言，这将直接影响氚向燃料循环的扩散。同样重要的是，液态金属在这些条件下以高流量运行。对液态金属磁流体动力学的精确模拟可以为更逼真的液态金属模拟和未来聚变反应堆的计算机辅助设计铺平道路。用传统的有限差分方法精确地模拟湍流需要非常精细的网格才能达到足够高的分辨率，而精确的解很快就会变得难以使用经典计算机进行计算。量子计算机提出了一种新的计算范式，当使用合适的量子算法时，它有可能加速计算任务，如求解某些偏微分方程(PDE)。这也促进了新颖的经典“量子启发”算法的发展。量子和量子启发算法用于求解偏微分方程组，在需要极高分辨率的场景建模中表现出很好的前景，如湍流。本项目旨在评估应用量子启发张量网络算法模拟液态金属流动的可行性。目前提出的求解非线性偏微分方程组的量子算法都是抽象的，不容易实现。这些算法通常解决比MHD方程更简单的偏微分方程组。提出的想法的一个特别的新颖性是包括了PDE中存在的洛伦兹力项，这在以前的量子或量子启发算法中从未被考虑过，并且对于准确地模拟聚变反应堆中的液态金属是必不可少的。该项目将专注于(经典地)实现、扩展和分析用于求解MHD方程的合适的量子启发张量网络算法，同时也对用于求解相关非线性偏微分方程组的现有纯量子算法进行概述和初步评估。实现和分析量子算法的一个关键目标是评估其相对于传统MHD方程解算器的潜在好处。此外，受量子启发的张量网络方法可以帮助评估在此可行性研究后最终实现量子实施的潜在好处和可行性。未来这些算法的成功部署可能会解决液态金属高分辨率模拟的挑战，加快新反应堆的工程周期，并有可能降低与实验测试相关的巨额成本。

This work addresses the computational challenge of simulating the magnetohydrodynamic equations of liquid metals such as Li or LiPb, which are used as coolants and sources of neutron multipliers and tritium breeding in nuclear fusion reactors. This project is a feasibility study into the use of quantum-inspired algorithms for simulating the magnetohydrodynamics of liquid metals, which are used as coolants and sources of tritium in nuclear fusion reactors. The fusion industry requires accurate predictions of liquid metal dynamics under high intensity magnetic fields.Simulating liquid metal flows within fusion reactors presents some specific challenges, due to the presence of phenomena such as turbulences induced by the magnetic fields present. In the case of tritium breeding in fusion reactors, this will directly influence the diffusion of tritium into the fuel cycle. It is also essential that liquid metals operate at high flow rates under these conditions. Accurate simulation of the magnetohydrodynamics of liquid metals could pave the way for more realistic simulation of liquid metals and computer-aided design of future fusion reactors.Modelling turbulences accurately with traditional finite difference methods requires very fine grids to achieve a high enough resolution, with accurate solutions quickly becoming computationally intractable using classical computers. Quantum computers present a new computational paradigm which has the potential to speed up computational tasks such as solving certain partial differential equations (PDEs) when using suitable quantum algorithms. This has also advanced novel classical “quantum-inspired” algorithms. Quantum and quantum-inspired algorithms for solving PDEs have shown promise in modelling scenarios which require extremely high resolutions, such as turbulence.This project aims to assess the feasibility of applying quantum-inspired tensor network algorithms for simulating liquid metal flows. Currently proposed quantum algorithms for solving nonlinear PDEs are formulated in an abstract way, which cannot readily be implemented. Those algorithms typically address simpler PDEs than the MHD equations. A specific novelty of the proposed idea is the inclusion of the Lorentz force term present in the PDE, which has not been considered in quantum or quantum-inspired algorithms before and is essential to accurately modelling liquid metals in fusion reactors. This project will focus on (classically) implementing, extending and analysing suitable quantum-inspired tensor network algorithms for solving the MHD equations while also producing an overview and initial assessment of existing pure quantum algorithms for solving relevant nonlinear PDEs. A key goal of the implementation and analysis of the quantum-inspired algorithm is an assessment of its potential benefits over traditional solvers for MHD equations. Furthermore, quantum-inspired tensor network methods can help assess the potential benefits and feasibility of an eventual quantum implementation after this feasibility study. Successful deployment of these algorithms in the future could address the challenges of high-resolution simulation of liquid metals, accelerate engineering cycles for new reactors and potentially reduce the massive costs associated with experimental testing.