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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…
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…
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 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…
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.…
We present a novel and efficient in terms of circuit depth design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) Draper's adders to build…
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 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…
We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory qubits and the number of operations required to perform factorization, using the algorithm…
The optimal design of a fault-tolerant quantum computer involves finding an appropriate balance between the burden of large-scale integration of noisy components and the load of improving the reliability of hardware technology. This balance…
We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous…
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…
Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and…
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…
We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Eker{\aa}-H{\aa}stad 2017,…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum…
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…
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…
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…