Related papers: Prime Factorization in the Duality Computer
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the…
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…
Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity…
Studying the factorization theory of numerical monoids relies on understanding several important factorization invariants, including length sets, delta sets, and $\omega$-primality. While progress in this field has been accelerated by the…
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…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…
Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…
The factorization of a large digit integer in polynomial time is a challenging computational task to decipher. The exponential growth of computation can be alleviated if the factorization problem is changed to an optimization problem with…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which…
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…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…