Quantum Software for a Digital Universe

科学的重大进步是以把过去被认为是固定的和绝对的世界的各个方面纳入它的范围为标志的，而现在却揭示出这些方面是动态的和偶然的。达尔文通过自然选择的进化过程发现了物种的起源，这就是一个最好的例子。爱因斯坦发现时空本身有自己的运动规律，它的行为与其中的物质相结合。这样的发现总是为进一步的问题打开了大门——在世界观转变之前是不可想象的——就时空而言，我们今天面临的问题具有深刻的宇宙学性质，涉及时空和量子物质之间的相互作用和最终关系。该项目将开发新的量子软件，即量子算法，在假设时空在某种程度上是数字的或离散的，并尊重洛伦兹不变性的情况下，解决有关早期宇宙、粒子天体物理学和黑洞的量子场论（QFT）的基本物理问题。该项目的基本物理目标是：i)发现离散性对相互作用的量子标量场理论（如早期宇宙中的暴胀）的扰动的影响，或者，模拟由演化中的离散宇宙的大爆炸前动力学引起的初始密度扰动；Ii)通过状态计数方法来解释黑洞的熵，其中状态是视界的离散状态；Iii)在数字时空背景下发现天体物理或宇宙学起源的量子粒子的现象学。注意到违反洛伦兹不变性的严格界限，我们将使用一个离散数据集，它可以支持连续时空近似，同时也是洛伦兹不变性。随机的、离散的偏序集或因果集就是这样的数据集。这样的数学对象很难用解析的方法来处理，而数值计算对于进步是至关重要的，特别是对于从现象学模型中获得可测试的预测。然而，数值方法也有其局限性，因为经典算法需要大量的计算能力和时间，特别是在与现象学相关的四维时空情况下。我们的方法是为那些使用量子算法的物理问题开发数值方法，至少对于昂贵的子程序，我们将优先考虑可以在嘈杂的中间尺度量子设备上实现的量子算法。我们将使用的技术包括：变分量子特征求解器，量子近似优化算法，量子退火和绝热量子计算，以及量子行走。我们的目标是，这些量子算法将为数字宇宙物理学的新研究提供与经典数值方法相比的优势，并在不久的将来成为研究和测试基础物理学进一步离散模型的重要工具。这些量子算法将首先在使用高性能计算的仿真环境中进行测试，特别是使用Archer2国家领先的设备。将考虑噪声对性能的影响，我们将推断以了解这些算法优于经典数值方法的尺度。最终，我们的目标是在物理设备上运行这些量子算法——数字量子计算机——一旦我们对潜在优势的信心建立起来，并获得合适的硬件。我们将通过与量子计算和模拟中心的合作，或通过与国家量子计算中心和参与英国国家量子技术计划的量子硬件公司（如Rigetti和IBM）接触，寻求获得在英国国家量子技术计划内开发的硬件的访问机会。

Major progress in science is marked by the bringing into its scope aspects of the world that had previously been considered to be fixed and absolute, but are revealed instead to be dynamical and contingent. Darwin's discovery of the origin of the species by the process of evolution by natural selection is a prime example, as is Einstein's discovery that spacetime itself has its own laws of motion that couple its behaviour to the matter within it. Such discoveries always open the door to further questions -- unthinkable before the shift in world-view -- and in the case of spacetime, we are confronted today with questions of a profound and cosmological nature involving the interaction and ultimate relationship between spacetime and quantum matter. This project will develop new quantum software, namely quantum algorithms, to address fundamental physical questions about quantum field theory (QFT) in the early universe, particle astrophysics and black holes on the assumption that spacetime is, at some level, digital or discrete and also respects Lorentz invariance. The fundamental physics aims of this project are: i) discover the effect of discreteness on perturbations of an interacting quantum scalar field theory such as the inflaton in the early universe and, alternatively, model initial density perturbations arising from pre-Big Bang dynamics of an evolving discrete cosmos; ii) account for the entropy of a black hole by a state counting method where the states are discrete states of the horizon; iii) discover phenomenology of quantum particles of astrophysical or cosmological origin in a digital spacetime background. Heeding the stringent bounds on violation of Lorentz invariance, we will use a discrete dataset that can underpin a continuum spacetime approximation and also be Lorentz invariant. A random, discrete partial order or causal set is such a dataset. Such a mathematical object is difficult to deal with analytically and numerical calculations are crucial for progress, especially for obtaining testable predictions from phenomenological models. The numerical methods, however, also have their limitations since classical algorithms require extensive computational power and time, especially in the phenomenologically relevant case of 4-dimensional spacetime.Our approach is to develop numerical methods for those physical questions, that use quantum algorithms, at least for expensive subroutines, and we will prioritise quantum algorithms that can be implemented on Noisy Intermediate Scale Quantum devices. The techniques we will use include: the variational quantum eigensolver, the quantum approximate optimisation algorithm, quantum annealing and adiabatic quantum computing, as well as quantum walks. The ambition is that these quantum algorithms will offer advantage in comparison with classical numerical methods for these novel investigations of the physics of a digital universe, and be an important tool for investigating and testing further discrete models for fundamental physics in the near-future. These quantum algorithms will first be tested in an emulation environment using High Performance Computing and specifically the Archer2 national leading facility. The effects of noise on the performance will be considered and we will extrapolate to understand the scales on which these algorithms will outperform classical numerical methods. Eventually, we aim to run these quantum algorithms on physical devices -- digital quantum computers -- once our confidence in the potential advantage is founded and access to suitable hardware is obtained. We will seek to obtain such access reaching out to hardware developed within the UK National Quantum Technology Programme: via our committed engagement with the Quantum Computing and Simulation Hub, or by approaching the National Quantum Computing Centre and quantum hardware companies involved in the UK National Quantum Technology Programme, such as Rigetti and IBM.