Simulation of Grover's quantum search algorithm in an Ising-nuclear-spin-chain quantum computer with first- and second-nearest-neighbour couplings

Abstract

We implement Grover's quantum search algorithm on a nuclear spin-chain quantum computer, taking Ising-type interactions between nearest and second-nearest neighbours into account. The performance of this implementation is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtain pronounced maxima at frequencies which fulfil the condition of the 2πk-method with respect to the second-nearest- neighbour interactions.

Study of Decoherence on the Teleportation Algorithm in a Chain of Three Nuclear Spins System

“…Our registers are made up of three qubits 2 1 0    and so on. The parameters used for our simulation are taken from [21] and are given (in units of ) as 24The selected teleported state is defined by the coefficients (13) of the state x . Assuming that the environment acts homogeneously on the qubits, the damping parameter can be the same for each qubit, and the damping parameter for correlated cases at second neighbors can be one order of magnitude weaker that at first neighbors.…”

“…. The unitary evolution of the system is denoted by k   , where    denotes the type of pulse of duration   [21].…”

“…In the first part of our work, we describe the model and the Hamiltonian of our quantum system, and we must point out that, although this Hamiltonian will be time explicitly dependent, if we consider weak interaction between our system and the environment (the characteristic times of the quantum system are much longer than those of the environment) as a first approximation, the above mentioned Markovian-Lindblad master type equation can be still used for our study [11,17,18]. One needs to mention that even this linear chain of three nuclear spins model for solid state quantum computer has not been built yet, it has been very useful for theoretical studies about implementation of quantum gates and quantum algorithms [19][20][21] which can be extrapolated to other solid state quantum computers [22,23]. After doing this, we establish the five cases to be considered with the quantum-environment system: independent environment interaction (A), pure dephasing interaction (B), correlated dissipation interaction (C), dephasing correlated interaction (D), and thermalization case (E).…”

Quasi non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer

“…The parameters used for our simulation are taken from [25] regarding the Larmor frequencies of the nuclear spins and we take a higher Ising coupling strength for modelling the differences between the Markovian and the quasi-non Markovian regime but maintaining the method [25]. These parameters are (in units of…”

Measurement-enhanced quantum search

“…One of the promising candidates is an Ising spin chain. Implementations of Grover's search and other quantum algorithms in an Ising spin chain are done in [7,8]. In this paper, we modify the quantum search algorithm applied to an Ising spin chain using radio frequency pulses to suppress the oscillation.…”