Related papers: Prime Factorization of Arbitrary Integers with a L…
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…
The isoenergetic cycle is a purely mechanical cycle comprised of adabatic and isoenergetic processes. In the latter the system interacts with an energy bath keeping constant the expectation value of the Hamiltonian. This cycle has been…
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…
State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to…
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,…
Factorization is the most fundamental way to determine if a number $n$ is prime or composite. Yet, this approach becomes impracticable when considering large values of $n$, a difficulty that is exploited by cryptographic protocols. We…
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,…
We study theoretically the quantum dynamics of an electron in the symmetric four-level double-dot structure under the influence of the monochromatic resonant pulse. The probability amplitudes of the eigenstates relevant for the quantum…
We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an alphabet where its structure is implied by the…
This paper proposes a new factorization algorithm for computing the phase factors of quantum signal processing. The proposed algorithm avoids root finding of high degree polynomials by using a key step of Prony's method and is numerically…
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly…
We show that the excitation probability of a state within a manifold of levels undergoes Rabi oscillations with frequency determined by the energy difference between the states and not by the pulse area for sufficiently strong pulses. The…
We investigate Rabi oscillation of an atom ensemble in Gaussian spatial distribution. By using the ultrafast laser interaction with the cold atomic rubidium vapor spatially confined in a magneto-optical trap, the oscillatory behavior of the…
Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular…
Quantum computation is a continuously growing research area which is based on nature and resources of quantum mechanics, as superposition and entanglement. In its quantum circuits version, the use of convenient and appropriate gates is…
The applicability of the factorization method is extended to the case of quantum fractional-differential Hamiltonians. In contrast with the conventional factorization, it is shown that the `factorization energy' is now a…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
For a one-dimensional chain of four nuclear spins (1/2) and taking into account first and second neighbor interactions among the spin system, we make the numerical simulation of Shor prime factorization algorithm of the integer number N=4…