Quantum Probability Spaces

Jincheng Zhang

Probability Space Quantum Machine Learning (PSML) represents a paradigm shift in machine learning, extending beyond traditional static models to leverage the inherent properties of quantum probability spaces. This research explores the potential of PSML to significantly enhance machine learning model performance, particularly through the optimization of models based on quantum feature spaces. The core claim of this work is that PSML not only facilitates quantum machine learning but actively refines models to improve generalization. This is achieved through the utilization of quantum probability spaces, offering a novel approach to optimization.

Sylvia Pulmannová

Massimo Melucci

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 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(n4) steps.

Miklós Rédei, Stephen J. Summers

Natarajan Shriethar

In the increasing traffic scenario and the presence of automated four-wheeler vehicle-like situations, we need to consider the possible safe driving for the two-wheelers also. As two-wheelers need manual balances, embedding the autopilot systems is a tougher task. To resolve this issue, we attempt to address this problem with probability spaces. Then, these classical probability spaces are promoted into quantum probability spaces. The quantum computing aspects such as quantum gates are embedded in the analysis of the quantum probability space. With those quantum computing protocols, various traffic scenarios are calculated, such as the probability of accidents and the avoidance probability of accidents. A set of mathematical lemmas with certain conditions and their proof for mapping classical to quantum probability space and the singularities in this quantum probability space are also discussed in this work.