Related papers: An n-bit general implementation of Shor's quantum …
This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…
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…
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…
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…
We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a…
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…
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…
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…
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…
Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the…
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.…
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 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…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
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…
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…
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…
The objective of this paper concerns at first the motivation and the method of Shor's algorithm including an excursion into quantum mechanics and quantum computing introducing an algorithmic description of the method. The corner stone of…
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 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…