相关论文: Semiclassical Shor's Algorithm

We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For…

Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…

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 algorithm of Shor for prime factorization is a hybrid algorithm consisting of a quantum part and a classical part. The main focus of the classical part is a continued fraction analysis. The presentation of this is often short, pointing…

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…

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…

Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification…

Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…

We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…

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 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…

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…

We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of…

We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…

The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…

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…

It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…

We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21.…

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…