相关论文: Shor's Quantum Factoring Algorithm

One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the…

We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the…

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…

Factoring integers is considered as a computationally-hard problem for classical methods, whereas there exists polynomial-time Shor's quantum algorithm for solving this task. However, requirements for running the Shor's algorithm for…

There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to…

Shor's algorithm (SA) is a quantum algorithm for factoring integers. Since SA has polynomial complexity while the best classical factoring algorithms are sub-exponential, SA is cited as evidence that quantum computers are more powerful than…

Continuous improvements in quantum computing hardware are exposing the need for simultaneous advances in software. Large-scale implementation of quantum algorithms requires rapid and automated compilation routines such as circuit synthesis…

We demonstrate that locally connected networks of machines that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of quantum computation. We present simulation results for basic quantum…

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…

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…

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…

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…

Project of an undergraduate student in physics (4th year) about the concept of quantum computers (QC) and its social impact. After a thourough theoretical introduction (chap. 2), the recent debate about NMR-based QC is dealt with in detail…

The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…

In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current…

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…

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…

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities.…

Shor's algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm, showing that the coherence in each step relies on the…

Shor's algorithm is one of the most prominent quantum algorithms, yet finding efficient implementations remains an active research challenge. While many approaches focus on low-level modular arithmetic optimizations, a broader perspective…