相关论文: Robustness of Shor's algorithm

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…

In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…

The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…

We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally…

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],…

Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…

A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of…

The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…

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…

Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…

The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…

This paper aims to determine the exact success probability at each step of Shor's algorithm. Although the literature usually provides a lower bound on this probability, we present an improved bound. The derived formulas enable the…

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…

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show…

We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a…

The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…

Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…

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…

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…

Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…