Related papers: Accelerating Shor's Factorization Algorithm on GPU…
Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how…
Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…
Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a…
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…
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…
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…
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…
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…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
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 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…
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…
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…
We show how the execution time of algorithms on quantum computers depends on the architecture of the quantum computer, the choice of algorithms (including subroutines such as arithmetic), and the ``clock speed'' of the quantum computer. The…
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…
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
Quantum computing represents a significant advancement in computational capabilities. Of particular concern is its impact on asymmetric cryptography through, notably, Shor's algorithm and the more recently developed Regev's algorithm for…
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-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and…