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Quantum random number generator (QRNG) relies on the intrinsic randomness of quantum mechanics to produce true random numbers which are important in information processing tasks. Due to the presence of the superposition state, a quantum computer can be used as a true random number generator. However, in practice, the implementation of the quantum computer is subject to various noise sources, which affects the randomness of the generated random numbers. To solve this problem, we propose a scheme based on the quantum computer which is motivated by the source-independent QRNG scheme in optics. By using a method to estimate the upper bound of the superposition state preparation error, the scheme can provide certified randomness in the presence of readout errors. To increase the generation rate of random bits, we also provide a parameter optimization method with a finite data size. In addition, we experimentally demonstrate our scheme on the cloud superconducting quantum computers of IBM. [ABSTRACT FROM AUTHOR]

The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimization of the quantum circuit for discrete logarithm of binary elliptic curves under a constrained connectivity, focusing on the resource expenditure and the optimal design for quantum operations such as the addition, binary shift, multiplication, squaring, inversion, and division included in the point addition on binary elliptic curves. Based on the space-efficient quantum Karatsuba multiplication, the number of CNOTs in the circuits of inversion and division has been reduced with the help of the Steiner tree problem reduction. The optimized size of the CNOTs is related to the minimum degree of the connected graph. [ABSTRACT FROM AUTHOR]