Related papers: Using Simulated Annealing to Factor Numbers
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His…
Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We…
Considering the large-scale quantum computer, it is important to know how much quantum computational resources is necessary precisely and quickly. Unfortunately the previous methods so far cannot support a large-scale quantum computing…
The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. The general construction of the Fourier transform on an Abelian group is outlined and this provides a…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…
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…
If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information…
Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both…
Shor's factoring algorithm (SFA) finds the prime factors of a number, $N=p_1 p_2$, exponentially faster than the best known classical algorithm. Responsible for the speed-up is a subroutine called the quantum order finding algorithm (QOFA)…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
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…
Determining the prime factors of a given number N is a problem, which requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by P. Shor for quantum computers. However, the realization of…
The evaluation of the performance of adiabatic annealers is hindered by lack of efficient algorithms for simulating their behaviour. We exploit the analyticity of the standard model for the adiabatic quantum process to develop an efficient…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…
As one of the most robust global optimization methods, simulated annealing has received considerable attention, with many variations that attempt to improve the cooling schedule. This paper introduces a variant of simulated annealing that…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also…