Related papers: Computing Shor's algorithmic steps with classical …
We present here a classical optics device based on an imaging architecture as analogy of a quantum system where the violation of the Bell inequality can be evidenced. In our case, the two qbits entangled state needed to obtain non classical…
We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and $35$. The semi-classical quantum Fourier transform is used to implement the algorithm…
Spin and orbital angular momenta of light are attractive resources to harness for encoding, and manipulating information, with applications in various quantum photonic technologies. However, to fully harness that potential, we require…
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…
We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged…
We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…
We investigate macroscopic entanglement of quantum states in quantum computers, where we say a quantum state is entangled macroscopically if the state has superposition of macroscopically distinct states. The index $p$ of the macroscopic…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
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…
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…
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…
The Fourier transform proves indispensable in the processing of classical information as well as in the quantum domain, where it finds many applications ranging from state reconstruction to prime factoring. An implementation scheme of the…
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…
The advent of increasingly precise gyroscopes has played a key role in the technological development of navigation systems. Ring-laser and fibre-optic gyroscopes, for example, are widely used in modern inertial guidance systems and rely on…
Classical deep learning algorithms have aroused great interest in both academia and industry for their utility in image recognition, language translation, decision-making problems and more. In this work, we have provided a quantum deep…
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The…
Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous…
In analogy with the spin-squeezing inequality of Wang and Sanders [Physical Review A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields, and whose violation…