Related papers: Shor's Algorithm Does Not Factor Large Integers in…

Grover's quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a…

We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits…

Shor's algorithm is examined critically from the standpoint of it's eventual use to obtain the factors of large integers.

We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical…

Quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era presents significant challenges in differentiating quantum software bugs from hardware noise. Traditional debugging techniques from classical software engineering cannot…

Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing,…

In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only 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…

The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated…

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…

Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term…

Quantum Computing (QC) promises computational speedup over classic computing for solving complex problems. However, noise exists in current and near-term quantum computers. Quantum software testing (for gaining confidence in quantum…

We consider frequency estimation in a noisy environment with noisy probes. This builds on previous studies, most of which assume that the initial probe state is pure, while the encoding process is noisy, or that the initial probe state is…

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…

The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform.…

Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…

When quantum programs are executed on noisy intermediate-scale quantum (NISQ) computers, they experience hardware noise; consequently, the program outputs are often erroneous. To mitigate the adverse effects of hardware noise, it is…

The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using…