Related papers: Practical Challenges in Executing Shor's Algorithm…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…
The number of qubits in quantum computers keeps growing, but most quantum programs remain relatively small because of the noisy nature of the underlying quantum hardware. This might lead quantum cloud providers to explore increased hardware…
Another threat is the development of large quantum computers, which have a high likelihood of breaking the high popular security protocols because it can use both Shor and Grover algorithms. In order to fix this looming threat,…
These are pedagogical notes on Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the…
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
The goal of this paper is to outline a general-purpose scalable implementation of Shor's period finding algorithm using fundamental quantum gates, and to act as a blueprint for linear optical implementations of Shor's algorithm for both…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that…
As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size…
We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…
Due to recent development in quantum computing, the invention of a large quantum computer is no longer a distant future. Quantum computing severely threatens modern cryptography, as the hard mathematical problems beneath classic public-key…
The software engineering community is facing challenges from quantum computers (QCs). In the era of quantum computing, Shor's algorithm running on QCs can break asymmetric encryption algorithms that classical computers practically cannot.…
Quantum Technologies is a term that is getting broader with every passing year. Nanotechnology and electronics operate in this realm. With the invention of industry-disrupting algorithms like Shor's algorithm that can break RSA encryption…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…