Evaluate Hamming Distance Using Quantum Computing

Hamming distance is a metric in information theory that is used to assess how many points a given signal is different from another. The smaller the Hamming distance, the more similar the signals. In classical digital systems, Hamming distance can be evaluated using XOR gates. In quantum computing, Hamming distance finds applications in domains like quantum information science (QIS) and quantum cryptography, where it is used to compare quantum data. However, since quantum computing employs an entirely different technology, quantum data encoded in quantum circuits needs an altogether different algorithm for evaluating the Hamming distance.

In this project, we’ll construct a quantum circuit to evaluate the Hamming distance between two statevectors. We’ll acquaint ourselves with the required tools, use them to construct the pertinent quantum circuit, and then test the functionality of the quantum circuit.