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In this work, trapped ultracold atoms are proposed as a platform for efficient quantum gate circuits and algorithms. We also develop and evaluate quantum algorithms, including those for the Simon problem and the black-box string-finding problem. Our analytical model describes an open system with non-Hermitian Hamiltonian. It is shown that our proposed scheme offers better performance (in terms of the number of required gates and the processing time) for realizing the quantum gates and algorithms compared to previously reported approaches.

Based on recent experiments [Nature 449, 438 （2007） and Nature Physics 6, 777 （2010）], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation times of such gates while functioning in algorithm applications depend on the number of photons present in their resonant cavities. Multi-qubit algorithms can be realized in systems in which the photon number is increased slightly over the qubit number. In addition, the time required for operation is considerably less than the dephasing and relaxation times of the systems. The contextual use of the photon number as a main control in the realization of any algorithm was demonstrated. The results indicate the possibility of a full integration into the realization of multi-qubit multiphoton states and its application in algorithm designs. Yhrthermore, this approach will lead to a successful implementation of these designs in future experiments.

A one-dimensional chain of long-range vibrational trapped ions at low phonon temperatures is employed to simulate the arising and robustness of the information of nonlocal correlations among correlated and uncorrelated sites. We demonstrate that the direction of the acting global magnetic field in Paul’s trap controls the dynamics of correlations and entanglement between ions. Also, we analyze the robustness of the nonlocal correlations in the trap under the impact of ions vibrating and the interaction strength of ions by considering the distance between them. The criteria of concurrence entanglement, Bell inequality, and uncertainty-induced nonlocality are studied to detect the nonlocal correlations among ions that decide the fundamental resources of information in the chain. Furthermore, the analytical solution describing the decoherence equation under the ionic vibration in Paul’s trap is found to track encoded information in the chain.

We analyze the dynamics of squeezing in a ballistic quantum wire with Rashba spin-orbit interaction in the presence of both strong and weak magnetic fields and for different initial states of the system. Compared to the more standard measure of squeezing based on variances, we show that entropy squeezing is a more sensitive measure. Our results show that there is a strong relationship between the spin-orbit interaction and the strength of entropy squeezing. Furthermore, there is a relationship between the initial state and the number of squeezed components. This allows new knobs to control the strength and the component of entropy squeezing in a nanowire system.

In this article, an analytical description is presented based on the master equation. This master equation is formed from the system of superconducting phase qubit which is coupled to a torsional resonator and damped by a dispersive reservoir. An analytical approach for searching of some physical phenomena on the qubit system is presented, such as qubit inversion, purity and negativity. In addition, these phenomena are discussed for the resonance and off-resonance cases for many different initial states. From computational results, it is found that the mentioned phenomena depend on the dispersive reservoir parameter which leads to their death. However, the complete destruction of system coherence in the presence of dispersive reservoir leads to the death of entanglement between the qubit and torsional resonator.

We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm.

This article discusses the potential engineering of entanglement propagation through two forms of spin ladders. In fact, future advances in quantum information will likely be guided by knowledge of quantum materials such as quantum spin systems, as was the case with the development of classical information technology throughout the previous century. Information transfer is a key use of spin systems, which are characterized by their reduced dimension. Spin ladders are a type of low-dimensional spin systems that exhibit interesting behavior between the extremes of one-dimensional chain and two-dimensional plane. The current work is dedicated to analyzing the performance of such structures in the field of quantum state transfer (QST). The purpose of this study was attained by paying attention to the dynamical behavior of entanglement and its measure (concurrence) in these systems, as this method permits an extensive understanding of the QST process. So that the signature of QST scenarios can be identified through the lens of concurrence propagation. Then, the configuration’s efficiency in the QST procedure is established by comparing the behavior of this measure as time passed in the two selected ladders. The optimal condition for the transfer of an entangled state is that the value of the concurrence function reaches unity for the target qubits at the certain time instants. Furthermore, the findings from both systems indicate the necessity of employing supplementary qubits in order to achieve a complete QST. In comparison with the inter-ladder interactions of qubits, the interactions between auxiliary qubits and the structure (intra-ladder interactions) must have comparatively weaker strength to enhance QST’s quality. The explanation for this phenomena is attributed to the notion of monogamy rule. In addition, it can be concluded that honeycomb ladders have a favorable QST process than two-leg ladders. Furthermore, we found that the larger sizes of systems need a higher amount of relative interactions to accomplish more effective transmission. Two-leg ladders, on the other hand, are more sensitive to increasing the system size.