Quantum Software for a Digital Universe

科学的重大进步的标志是将以前被认为是固定的和绝对的世界的一些方面纳入其范围，但事实表明，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物种起源就是一个很好的例子，爱因斯坦发现时空本身也有自己的运动定律，将它的行为与其中的物质联系在一起。这样的发现总是为进一步的问题打开大门--这在世界观转变之前是不可想象的--就时空而言，我们今天面临着涉及时空和量子物质之间的相互作用和最终关系的深刻的宇宙学性质的问题。该项目将开发新的量子软件，即量子算法，以解决关于早期宇宙中的量子场论(QFT)、粒子天体物理学和黑洞的基本物理问题，前提是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。这个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论(如早期宇宙中的膨胀子)微扰的影响，或者，模拟由演化的离散宇宙的大爆炸前动力学引起的初始密度微扰；ii)通过态计数方法解释黑洞的熵，其中的态是视界的分立态；iii)在数字时空背景中发现起源于天体物理或宇宙的量子粒子的唯象。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的数据集，它可以支持连续统时空近似，也可以是洛伦兹不变量。随机、离散的偏序或因果集就是这样的数据集。这样的数学对象很难分析处理，而数值计算对进展至关重要，特别是对于从现象学模型中获得可检验的预测。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，特别是在现象相关的4维时空的情况下。我们的方法是为这些物理问题开发数值方法，使用量子算法，至少对于昂贵的子例程，我们将优先考虑可以在有噪声的中等尺度量子设备上实现的量子算法。我们将使用的技术包括：变分量子本征解，量子近似优化算法，量子退火法和绝热量子计算，以及量子漫步。他们的抱负是，这些量子算法将为这些数字宇宙物理的新研究提供与经典数值方法相比的优势，并成为在不久的将来研究和测试基础物理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Archer2国家领先设施。我们将考虑噪声对性能的影响，并进行外推，以了解这些算法的性能将在多大程度上超过经典的数值方法。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--一旦我们建立了对潜在优势的信心，并获得了合适的硬件。我们将寻求接触英国国家量子技术计划内开发的硬件：通过我们与量子计算和模拟中心的承诺合作，或通过接触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。

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.