Related papers: Using Shor's algorithm on near term Quantum comput…
Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys…
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…
Shor's algorithm, which given appropriate hardware can factorise an integer $N$ in a time polynomial in its binary length $L$, has arguable spurred the race to build a practical quantum computer. Several different quantum circuits…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
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…
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…
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance…
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…
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…
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 try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…
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,…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…
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…
Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a…
Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification…