Related papers: Benchmarks for quantum computers from Shor's algor…

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…

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…

Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…

We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…

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…

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…

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…

As quantum computers grow in size and scope, a question of great importance is how best to benchmark performance. Here we define a set of characteristics that any benchmark should follow -- randomized, well-defined, holistic, device…

Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire…

The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely…

It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.

An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…

Quantum computer is no longer a hypothetical idea. It is the worlds most important technology and there is a race among countries to get supremacy in quantum technology. Its the technology that will reduce the computing time from years to…

Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…

These are pedagogical notes on Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the…

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…

Quantum coherence constitutes a fundamental physical mechanism essential to the study of quantum algorithms. We study the coherence and decoherence in generalized Shor's algorithm where the register $A$ is initialized in arbitrary pure…

The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of…

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…