Related papers: An integer factorization algorithm which uses diff…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
Let n be any odd natural number other than a perfect square, in this article it is demonstrated that this new factorization algorithm is much more efficient than the implementation technique [2,3 p.1470], described in this article, of the…
Let $n = \mathrm{p}\!\cdot\!\mathrm{q}$ (p < q) and $\Delta = \lvert p-q \rvert$, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any…
The challenges of graph stream algorithms are twofold. First, each edge needs to be processed only once, and second, it needs to work on highly constrained memory. Diffusion degree is a measure of node centrality that can be calculated (for…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
The largest number factored on a quantum device reported until now was 143. That quantum computation, which used only 4 qubits at 300K, actually also factored much larger numbers such as 3599, 11663, and 56153, without the awareness of the…
We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We…
We report a quantum-classical hybrid scheme for factorization of bi-prime numbers (which are odd and square-free) using IBM's quantum processors. The hybrid scheme proposed here involves both classical optimization techniques and adiabatic…
In this note we consider optimised circuits for implementing Shor's quantum factoring algorithm. First I give a circuit for which none of the about 2n qubits need to be initialised (though we still have to make the usual 2n measurements…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…