Related papers: Factoring integers via Schnorr's algorithm assiste…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
The aim of this paper is to elucidate the implications of quantum computing in present cryptography and to introduce the reader to basic post-quantum algorithms. In particular the reader can delve into the following subjects: present…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
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…
We construct an analog computer based on light interference to encode the hyperbolic function f({\zeta}) = 1/{\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
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…
Quantum computing has a potential to accelerate the data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general,…
The promise of quantum computation and its consequences for complexity-theoretic cryptography motivates an immediate search for cryptosystems which can be implemented with current technology, but which remain secure even in the presence of…
It is well known, and appreciated, that quantum computers have the potential to be the most powerful computational devices ever created. This newfound power comes from a quantum parallelism effect that allows the computer to be in multiple…
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
Shor's algorithm (SA) is a quantum algorithm for factoring integers. Since SA has polynomial complexity while the best classical factoring algorithms are sub-exponential, SA is cited as evidence that quantum computers are more powerful than…
Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and…
The quantum multicomputer consists of a large number of small nodes and a qubus interconnect for creating entangled state between the nodes. The primary metric chosen is the performance of such a system on Shor's algorithm for factoring…
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…
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…
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation…
Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical…
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
This work is a tutorial on Shor's factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for non-specialists which have basic knowledge on…