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The so-called Hamming distance measures the difference between two binary strings A and B. In simplified form, it measures the number of changes in A to get B. This type of distance is very useful in classical computing in applications such as error correction. It is also advantageous in quantum computing, being for example widely used in quantum machine learning. Since current quantum computers have limited resources, this type of distance is particularly attractive because it can be computed using fewer qubits and operations than other distances such as Euclidean or Manhattan distances. In this paper, two circuits for calculating Hamming distances using exclusively Clifford+T gates are presented. The aim of both circuits is to reduce the quantum cost and number of T gates needed to compute the Hamming distance. The T gate is more expensive than the other gates, so this reduction will have a significant impact on the total cost of the circuits. Furthermore, the proposed circuits are implemented using only Clifford+T gates. The circuits implemented exclusively with this group of gates are compatible with proven error detection and correction codes. [ABSTRACT FROM AUTHOR]

Topologically associating domains (TADs) are the most fundamental elements and significant structures of the eukaryotic genome. Currently, algorithms have been developed to find the TADs. But few algorithms are reported to compare the similarity of TADs between genomes. In this study, mice Hi-C sequencing data of four contrasts were enrolled. Seventeen algorithms, including BPscore, Jaccard index (JI) distance, VI distance, image hash, image subtraction, image variance, and so on, were used to quantify the genomic similarity of TADs. Image subtraction, Euclidean distance, and Manhattan distance were significantly better for TAD difference detection than the others. Deferent Hash (dHash) with the best zoom size ranked the second, followed by improved Hamming distance algorithm and JI distance. Advantages and disadvantages of various algorithms for quantifying the similarity of TADs were compared. Our work could provide the fundament for TADs comparison. [ABSTRACT FROM AUTHOR]