Related papers: Quantum factorization of 56153 with only 4 qubits
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
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…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical…
We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr\"obner bases. We present a novel scalable algorithm which combines the two approaches and leads to the…
In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…
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…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…
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…
There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation)…
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($k\geq 3$) terms to quadratic terms…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
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…
The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
Computations show that the logic about a quantum factoring algorithm does not hold in reality on a D-Wave quantum computer. We demonstrate this for the integers 15 = 3 x 5, 91 = 7 x 13 and 899 = 29 x 31. The likely cause is the D-Wave…