Related papers: Experimental prime factorization via the feedback …
Inspired by non-abelian vortex anyons in spinor Bose-Einstein condensates, we consider the quantum double $\mathcal{D}(Q_8)$ anyon model as a platform to carry out a particular instance of Shor's factorization algorithm. We provide the…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the…
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…
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…
We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…
Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but these are only useful if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
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 quantum multicomputer consists of a large number of small nodes and a qubus interconnect for creating entangled state between the nodes. The primary metric chosen is the performance of such a system on Shor's algorithm for factoring…
The largest number factored on a quantum device reported until now was 143. That quantum computation, which used only 4 qubits at 300K, actually also factored much larger numbers such as 3599, 11663, and 56153, without the awareness of the…
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…
In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…
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…
It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to…
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…
We implement a quantum protocol for prime number identification based on entanglement dynamics, using IBM quantum processors. The method links the primality of an integer to specific Fourier components extracted from the time evolution of…