Related papers: Factoring $2048$ bit RSA integers with a half-mill…

A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…

The aim of this work is to show a brand-new way of making deterministic Quantum Computing (short QC), in the sense of Theory of Calculability, by meaning of unitary evolution. We start from the original Shor's Algorithm to explain how the…

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…

Modern-day computer security relies heavily on cryptography as a means to protect the data that we have become increasingly reliant on. The main research in computer security domain is how to enhance the speed of RSA algorithm. The…

We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…

Almost all public secure communication relies on the inability to factor large numbers. There is no known analytic or classical numeric method to rapidly factor large numbers. Shor[1] has shown that a quantum computer can factor numbers in…

The realisation of utility-scale quantum computing inextricably depends on the design of practical, low-overhead fault-tolerant architectures. We introduce the Pinnacle Architecture, which uses quantum low-density parity check (QLDPC) codes…

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…

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…

A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…

We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring…

We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…

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…

To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT…

In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on…

We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the…

Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level.…

We investigate how to attack Shor's quantum algorithm for factorization with an entangling probe. We show that an attacker can steal an exact solution of Shor's algorithm outside an institute where the quantum computer is installed if he…

We contribute a 2D nearest-neighbor quantum architecture for Shor's algorithm to factor an $n$-bit number in $O(\log^2(n))$ depth. Our implementation uses parallel phase estimation, constant-depth fanout and teleportation, and…

This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout…