We propose the algorithm for the quantum computer on the IBM Q platform. By this algorithm one can obtain the multiple-quantum NMR dynamics of the dimer with spins 1/2. Our algorithm includes preparation of thermodynamic equilibrium state as initial conditions for dimer and circuit for evolution under the Hamiltonian of multiple-quantum NMR experiment. Multiple-quantum coherences arise in multiple-quantum NMR experiment. Ones are connected with solid body structure and get a lot of research consequently. Intensities of these coherences are measured at end of experiment. In our algorithm the intensities of multiple-quantum coherences are evaluated by tomography of diagonal elements of final density matrix for dimer.
In the present work the generation of entanglement between the receiver and sender is investigated in the process of the quantum state transfer in the homogeneous one-dimensional chain of spins 1/2 with the XY -Hamiltonian in the approximation of the nearest neighbour interactions. Fidelity is obtained for a quantum state transfer for various numbers of spins and temperatures and values of initial polarisation of the sender’s spin. The transmitted pure state is encoded in the state of first spin (sender) in the initial time moment. The other spins are in the thermodynamic equilibrium state. The reduced density matrix for the receiver and the sender is obtained for an investigation of entanglement in the “sender-receiver” system. The effect of temperature and polarization of the transmitted state on the generation of entanglement in the system is also investigated.
Quantum entanglement is a measure of quantum correlations which are responsible for effective work of quantum devices (in particular, quantum computers), significantly outperforming their classical counterparts.1 Here, we investigate quantum entanglement in the trimer clusters consisting of three electron spins sited in vertexes of an isosceles triangle. We consider entanglement of two subsystems of the system. The first subsystem consists of spins sited on the triangle baseline and the second subsystem consists of a spin equidistant from others. We generalized the Bleany-Bowers equation2, 3 for trimer clusters. It is shown that entanglement can emerge only in the case of the antiferromagnetic interaction of the subsystems. An equation for the temperature of the entanglement emergence is derived. The criterion of the double negativity4 is used in order to find the dependence of the entanglement on the temperature.
Quantum correlations in multiple quantum (MQ) NMR experiments are investigated in two-spin systems (dimers). In the initial moment of time one spin is in a pure quantum polarized state and the other spin is in the thermodynamic equilibrium state defined by the temperature of the sample. MQ NMR dynamics of dimers is investigated. It is shown that MQ NMR coherences of only the zeroth and second orders emerge in such a system. The intensities of those coherences are calculated. Entangled states appear in the course of the system evolution in the MQ NMR experiment. The quantum discord is obtained in the high temperature approximation.
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