Related papers: Implementation of Shor's Algorithm on a Linear Nea…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
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…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because…
In this article we develop an algorithm which computes a divisor of an integer $N$, which is assumed to be neither prime nor the power of a prime. The algorithm uses discrete time heat diffusion on a finite graph. If $N$ has $m$ distinct…
Shor's factoring algorithm provides a super-polynomial speed-up over all known classical factoring algorithms. Here, we address the question of which quantum properties fuel this advantage. We investigate a sequential variant of Shor's…
The quantum circuit model allows gates between any pair of qubits yet physical instantiations allow only limited interactions. We address this problem by providing an interaction graph together with an efficient method for compiling quantum…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
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…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package…
The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to…
Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their…
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…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
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…