A Quantum Probabilistic Comparator: Circuit Implementation

Decision making in stochastic autonomous systems, which considers uncertainty of many factors, is always a challenge. The problem can typically be addressed by probabilistic methods such as approximate stochastic optimization or Monte Carlo (MC) simulation. The potential solution may usually be constrained by the system's computing power, due to the size of the probabilistic problem. This paper aims to present and implement a quantum probabilistic comparison (QPC) algorithm that can help to find a desired solution or make decision between two random variables under uncertainty. This approach takes advantage of quantum computing to perform parallel comparison and fast calculation of the probability of matched state vectors. In the presented scheme, two random variables have different values (e.g., 2, 4, 8, or more values) and different probability distributions. The data of the variables are encoded to the basis states of the corresponding qubits. The quantum probabilistic comparator is used to make up the quantum output matrix that stores the comparison solutions as well as their probability probabilities. Moreover, unlike the existing quantum comparator algorithm, which uses bit string comparison approaches, the proposed probabilistic comparator is not only comparing the basis state, but also accumulating the outcome's probabilities. The calculation results of the quantum probabilistic comparator circuit are compared with those from classical computation and quantum circuit simulation as well as on an IBM quantum computer, for analysis and verification.