Related papers: Scalable semi-classical implementation of Shor fac…
Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical…
Time-multiplexed networks of degenerate optical parametric oscillators have demonstrated remarkable success in simulating coupled Ising spins, thus providing a promising route to solving complex combinatorial optimization problems. In these…
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 determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…
We optimize the pulse shape and polarization of time-dependent electric fields to maximize the production of electron-positron pairs via strong field quantum electrodynamics processes. The pulse is parametrized in Fourier space by a…
Many hard combinatorial problems can be mapped onto Ising models, which replicate the behavior of classical spins. Recent advances in probabilistic computers are characterized by parallelization and the introduction of novel hardware…
A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling…
Classical public-key cryptography standards rely on the Rivest-Shamir-Adleman (RSA) encryption protocol. The security of this protocol is based on the exponential computational complexity of the most efficient classical algorithms for…
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…
Recently, Cai showed that Shor's quantum factoring algorithm fails to factor large integers when the algorithm's quantum Fourier transform (QFT) is corrupted by a vanishing level of random noise on the QFT's precise controlled rotation…
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…
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…
We experimentally implement an optical algorithm for integration of a real-valued bivariate func- tion. A user-defined function is encoded in the position-dependent phase of one of the polarization components of an optical beam. The…
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…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
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…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
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…
We report a quantum-classical hybrid scheme for factorization of bi-prime numbers (which are odd and square-free) using IBM's quantum processors. The hybrid scheme proposed here involves both classical optimization techniques and adiabatic…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…