EPSRC Reference: 
EP/V047507/1 
Title: 
Architectures and Distribution Arithmetic for Coupling Classical Computers to Noisy IntermediateScale Quantum Computers 
Principal Investigator: 
StanleyMarbell, Professor P 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Engineering 
Organisation: 
University of Cambridge 
Scheme: 
Standard Research  NR1 
Starts: 
04 January 2021 
Ends: 
03 January 2023 
Value (£): 
202,190

EPSRC Research Topic Classifications: 
Statistics & Appl. Probability 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
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 increasinglyimportant 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 (floatingpoint 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 floatingpoint representations which serve as approximations of real numbers. Compact bitlevel representations for joint probability distributions and efficient methods to perform arithmetic on them could have farreaching impact on future computing systems in much the same way digital arithmetic and floatingpoint 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 inprocessor 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 bitlevel number representations that can efficiently capture the properties of probability distributions that contain lowprobability events which contribute significantly to the moments of a distribution; (2) new insights into the relationship between existing commonlyused 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 IntermediateScale 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 modelpredictive 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.

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