Related papers: Enhanced Scalability in Assessing Quantum Integer …

Shor's algorithm (SA) is a quantum algorithm for factoring integers. Since SA has polynomial complexity while the best classical factoring algorithms are sub-exponential, SA is cited as evidence that quantum computers are more powerful than…

The RSA cryptosystem could be easily broken with large scale general purpose quantum computers running Shor's factorization algorithm. Being such devices still in their infancy, a quantum annealing approach to integer factorization has…

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a…

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…

We propose an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom, and the capability of the quantum computer to perform desired tasks is monitored and gradually improved by…

Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…

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…

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…

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…

A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…

We present a method for mitigating measurement errors on quantum computing platforms that does not form the full assignment matrix, or its inverse, and works in a subspace defined by the noisy input bit-strings. This method accommodates…

Shor's algorithm is examined critically from the standpoint of it's eventual use to obtain the factors of large integers.

Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step…

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…

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],…

The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…

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…

Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…