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

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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.