An Efficient Algorithm to Compute a Quantum Probability Space

Abstract

Learning algorithms based on probability organize the observed data in subsets corresponding to binary variables. In this paper, we address the problem of estimating one probability space given a set of observed data about $n$n variables or properties. One problem with estimating one single probability space is the exponential number of events. Approximation is one approach to addressing the problem of the exponential order of the number of events. Alternatively to approximation, we change paradigm – from classical, set-based probability spaces based on sets to quantum probability spaces based on vector subspaces. By changing paradigm, we leverage quantum probability and present an efficient algorithm to calculate a Quantum Probability Space (QPS) in only $O(n^4)$O(n4) steps.