Related papers: Shor's Quantum Factoring Algorithm

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 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…

This paper studies one of the best known quantum algorithms - Shor's factorisation algorithm - via categorical distributivity. A key aim of the paper is to provide a minimal set of categorical requirements for key parts of the algorithm, in…

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…

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…

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…

To see the feasibility of a large-scale quantum computing, it is required to accurately analyze the performance and the quantum resource. However, most of the analysis reported so far have focused on the statistical examination, i.e.,…

A refinement of Shor's Algorithm for determining order is introduced, which determines a divisor of the order after any one run of a quantum computer with almost absolute certainty. The information garnered from each run is accumulated to…

We propose a semiclassical version of Shor's quantum algorithm to factorize integer numbers, based on spin-1/2 SU(2) generalized coherent states. Surprisingly, we find evidences that the algorithm's success probability is not too severely…

Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…

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…

The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…

In this note we consider optimised circuits for implementing Shor's quantum factoring algorithm. First I give a circuit for which none of the about 2n qubits need to be initialised (though we still have to make the usual 2n measurements…

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…

Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…

The lecture notes contain three parts. The first part is Grover's Search Algorithm with modifications, generalizations, and applications. The second part is a discussion on the quantum fingerprinting technique. The third part is Quantum…

Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…

This paper aims to determine the exact success probability at each step of Shor's algorithm. Although the literature usually provides a lower bound on this probability, we present an improved bound. The derived formulas enable the…

Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity…

Very recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. In this note, we remark that the report is somewhat misleading because there…