A Quantum Algorithm for Evaluating the Hamming Distance
Sohail Khan, Mohammad Nauman, Suleiman Ali Alsaif, Toqeer Ali Syed, Hassan Ahmad Eleraky
Abstract
We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary qubits. In particular, we use the power of the entanglement degree based quantum computing model that preserves at most the locality of interactions within the quantum model structure. This model uses one of two techniques to retrieve the solution of a quantum computing problem at hand. In the first technique, the solution of the problem is obtained based on whether there is an entanglement between the two ancillary qubits or not. In the second, the solution of the quantum computing problem is obtained as a function in the concurrence value, and the number of states that can be generated from the Boolean variables. The proposed algorithm receives two oracles, each oracle represents an unknown Boolean function, then it measures the hamming distance between these two oracles. The hamming distance is evaluated based on the second technique. It is shown that the proposed algorithm provides exponential speedup compared with the classical counterpart for Boolean functions that have large numbers of Boolean variables. The proposed algorithm is explained via a case study. Finally, employing recently developed experimental techniques, the proposed algorithm has been verified using IBM's quantum computer simulator.