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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]

Current quantum computers have a limited number of resources and are heavily affected by internal and external noise. Therefore, small, noise-tolerant circuits are of great interest. With regard to circuit size, it is especially important to reduce the number of required qubits. Concerning to fault-tolerance, circuits entirely built with Clifford+T gates allow the use of error correction codes. However, the T-gate has an excessive cost, so circuits with a high number of T-gates should be avoided. This work focuses on optimising in such terms an operation that is widely used in larger circuits and algorithms: the calculation of the absolute-value of two's complement encoded integers. The proposed circuit halves the number of required T gates with respect to the best circuit currently available in the literature. Moreover, our circuit requires at least 2 qubits less than the other circuits for such an operation. [ABSTRACT FROM AUTHOR]

Generating random numbers is important for many real-world applications, including cryptography, statistical sampling and Monte Carlo simulations. Quantum systems subject to a measurement produce random results via Born's rule, and thus it is natural to study the possibility of using such systems in order to generate high-quality random numbers. However, current quantum devices are subject to errors and noise, which can make the output bits deviate from the uniform distribution. In this work, we propose and analyse two protocols that can be used to increase the uniformity of the bits obtained when running a circuit with a Hadamard gate and a measurement in a noisy quantum computer. These protocols may be used prior to other standard processes, such as randomness amplification. We conduct experiments on both a quantum simulator and a real quantum computer, obtaining results that suggest that these protocols are useful to improve the probability of the generated bits passing statistical tests for uniformity. [ABSTRACT FROM AUTHOR]