Architectures and Distribution Arithmetic for Coupling Classical Computers to Noisy Intermediate-Scale Quantum Computers

所有的物理测量都有测量不确定度，最好用概率分布表示。从传感器到机器学习算法的测量，以及对量子计算硬件输出的测量以获得最终结果，这些都是这一概念在研究和工业中日益重要的应用的例子。测量的分布性质和测量应用的重要性使得计算系统能够直接对概率分布的表示执行算术运算越来越有价值，类似于它们对实数的近似表示(浮点算术)执行计算的能力。然而，创建最终可以在数字微处理器体系结构中实现的数字表示以及用于算术和逻辑的相关数学方法仍然是一个悬而未决的研究挑战，以使未来的计算机能够对概率分布执行算术和逻辑运算。以此类推，构成现代世界大多数技术基础的微处理器对整数和浮点表示进行算术运算，作为实数的近似。联合概率分布的紧凑位级表示和对其执行算术的有效方法可能会对未来的计算系统产生深远的影响，就像数字算术和浮点数表示构成了今天微处理器的基础一样。分布计算还可以实现全新的应用，如神经网络，它跟踪网络权重中的认知不确定性以及输入和预测中的任意不确定性。我们的研究目标是探索概率分布的高效处理器内表示的新前沿，从而使新的计算系统能够在本地执行概率分布的算术和逻辑。我们将研究：(1)新的比特级数字表示，它可以有效地捕捉包含对分布矩有显著贡献的低概率事件的概率分布的特性；(2)对现有常用的分布距离度量与表征分布之间差异的新方法之间的关系的新见解；(3)对分布进行算术和逻辑运算的新数学方法，其速度比对联合概率分布执行蒙特卡罗模拟的事实标准快数量级。从长远来看，我们的研究结果可能会对未来的贝叶斯机器学习方法产生变革，并可能从根本上实现新的微处理器体系结构，以处理噪声中尺度量子(NISQ)计算机的分布输出。从中期来看，我们研究的方法可以应用于广泛的基础科学挑战，从用于加速添加剂制造中沉淀过程中颗粒尺寸分布的现场计算建模和模型预测控制的新计算机硬件体系结构，到用于加快制药研究中结晶过程颗粒尺寸分布计算建模的新计算机硬件体系结构。

All physical measurements have measurement uncertainty and are best represented with probability distributions. Measurements from sensors feeding machine learning algorithms and measurements of the outputs of quantum computing hardware to obtain their final results are examples of increasingly-important applications of this concept in both research and industry. The distributional nature of measurements and the importance of the applications of measurements makes it increasingly valuable for computing systems to be able to perform arithmetic directly on representations of probability distributions, analogous to their ability to perform computations on approximate representations of real numbers (floating-point arithmetic).There however remains an unsolved research challenge to create number representations, and associated mathematical methods for arithmetic and logic, that could eventually be implemented in digital microprocessor architectures to enable computers of the future to perform arithmetic and logic operations on probability distributions. By analogy, microprocessors, which form the foundation of most of the modern world's technologies, perform arithmetic on integers and floating-point representations which serve as approximations of real numbers. Compact bit-level representations for joint probability distributions and efficient methods to perform arithmetic on them could have far-reaching impact on future computing systems in much the same way digital arithmetic and floating-point number representations have formed the foundation for today's microprocessors. Computation on distributions could also enable fundamentally new applications such as neural networks that track epistemic uncertainty in their network weights and aleatoric uncertainty in their inputs and predictions.Our research objective is to explore new frontiers in efficient in-processor representations of probability distributions that could enable new classes of computing systems that natively perform arithmetic and logic on probability distributions. We will investigate: (1) new bit-level number representations that can efficiently capture the properties of probability distributions that contain low-probability events which contribute significantly to the moments of a distribution; (2) new insights into the relationship between existing commonly-used distribution distance metrics and new methods for characterizing the differences between distributions; (3) new mathematical methods for performing arithmetic and logic on distributions, which are orders of magnitude faster than the de facto standard of performing Monte Carlo simulations on joint probability distributions.In the long term, the results of our investigation could be transformative for future Bayesian machine learning methods and could enable fundamentally new microprocessor architectures for processing the distributional outputs of Noisy Intermediate-Scale Quantum (NISQ) computers. In the medium term, the methods we investigate could be applied across a broad range of fundamental scientific challenges, from new compute hardware architectures for accelerating in situ computational modeling and model-predictive control of the distribution of particle sizes in precipitation processes occurring in additive manufacturing, to new compute hardware architectures for accelerating the computational modeling of particle size distributions in crystallization processes for pharmaceuticals research.