Related papers: Demonstration of Shor's quantum factoring algorith…

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…

In this paper, we briefly discuss the methodology for simulating a quantum computer which performs Shor's algorithm on a 7-qubit system to factorise 15. Using this simulation and the overlooked quantum brachistochrone method, we devised a…

A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…

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…

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…

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…

Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with…

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…

The purpose of this note was to give a proof that Shor's algorithm for period search is polynomial using only the standard $2^{n}$ quantum Fourier thansform and some simple trigonometry. There is an error that was pointed out to the author…

A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of…

Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…

The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated…

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…

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…

Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…

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 present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…

We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The…