相关论文: Factoring in a Dissipative Quantum Computer

The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…

Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…

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…

Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…

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],…

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…

We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The…

Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…

This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the…

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…

We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…

Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved 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…

With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…

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…

Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a…

We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…

Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how…

The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…