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，如锂或锂铅，这是用来作为冷却剂和源的中子倍增器和氚增殖的核聚变反应堆的磁流体动力学方程的计算挑战。该项目是一项可行性研究，探讨利用量子启发算法模拟液态金属的磁流体动力学，液态金属在核聚变反应堆中用作冷却剂和氚源。聚变工业需要精确预测高强度磁场下的液态金属动力学。由于存在磁场诱导的超导现象，模拟聚变反应堆内的液态金属流动存在一些特定的挑战。在聚变反应堆中氚增殖的情况下，这将直接影响到氚在燃料循环中的扩散。同样重要的是，液态金属在这些条件下以高流速运行。液态金属磁流体动力学的精确模拟可以为液态金属更真实的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模拟磁流体动力学需要非常精细的网格来达到足够高的分辨率，而精确的解很快就变得难以使用经典计算机计算。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，例如求解某些偏微分方程（PDE）。这也推动了新颖的经典“量子启发”算法。用于求解偏微分方程的量子和量子启发算法在模拟需要极高分辨率的场景（例如湍流）方面显示出了希望。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的量子算法是以抽象的方式制定的，这不能容易地实现。这些算法通常处理比MHD方程更简单的偏微分方程。所提出的想法的一个具体的新奇是包含存在于PDE中的洛伦兹力项，这在量子或量子启发的算法中还没有被考虑过，并且对于精确地模拟聚变反应堆中的液体金属至关重要。该项目将专注于（经典地）实现，扩展和分析合适的量子启发张量网络算法来解决MHD方程，同时还对现有的纯量子算法进行概述和初步评估，以解决相关的非线性偏微分方程。量子启发算法的实现和分析的一个关键目标是评估其相对于传统MHD方程求解器的潜在优势。此外，量子启发的张量网络方法可以帮助评估在此可行性研究之后最终量子实现的潜在好处和可行性。未来这些算法的成功部署可以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.