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arXiv:0903.2705

Controlled multiqubit entangled states and quantum transmission in quantum molecule-spin systems

Xiang Hao, Tao Pan, Taocheng Zang, Shiqun Zhu

Published Mar 16, 2009• 0 citations
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Abstract

he multiqubit entangled states are coherently controlled in the quantum spin systems composed of $N+1$ interacting antiferromagnetic molecular rings. The tunable intermolecular couplings arise from the local exchange interactions between electron spins of $N$ circumjacent magnets and those of one central molecular ring. The quantum dynamics of such system is analytically deduced by the effective spin hamiltonian with anisotropic Heisenberg couplings. It is found that entangled $W$ states can be generated with a high precision under the circumstance of quantum fluctuations. The multiqubit entangled state is also transferred from some molecular rings to others by the selection of intermolecular couplings.

DOI
10.48550/arxiv.0903.2705

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he multiqubit entangled states are coherently controlled in the quantum spin systems composed of N+1N+1N+1 interacting antiferromagnetic molecular rings. The tunable intermolecular couplings arise from the local exchange interactions between electron spins of NNN circumjacent magnets and those of one central molecular ring. The quantum dynamics of such system is analytically deduced by the effective spin hamiltonian with anisotropic Heisenberg couplings. It is found that entangled WWW states can be generated with a high precision under the circumstance of quantum fluctuations. The multiqubit entangled state is also transferred from some molecular rings to others by the selection of intermolecular couplings.
The multiple entangled states are controlled in the spin quantum systems composed of N+1 interacting antifer-romagnetic molecular rings.The tunable intermolecular couplings arise from the exchange interactions between electron spins of N circumjacent magnets and those of a central molecular ring.The quantum dynamics of such a system is deduced through the analysis of the effective spin hamiltonian with anisotropic Heisenberg couplings.It is found that an entangled W state can be generated precisely under the circumstance of quantum fluctuations.The multiple entangled state can also be transferred from some molecular rings to others by the manipulation of intermolecular couplings
Antiferromagnetic spin rings represent prototypical realizations of highly correlated, low-dimensional systems. Here we theoretically show how the introduction of magnetic defects by controlled chemical substitutions results in a strong spatial modulation of spin-pair entanglement within each ring. Entanglement between local degrees of freedom (individual spins) and collective ones (total ring spins) are shown to coexist in exchange-coupled ring dimers, as can be deduced from general symmetry arguments. We verify the persistence of these features at finite temperatures, and discuss them in terms of experimentally accessible observables.
Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field.
This thesis studies four related projects: tuning entanglement for spin systems, de-coherence and dynamics of entanglement, entanglement as measure of electron correlation in chemical systems and quantum algorithms to search for global minima. Chapter 1 presents a general introduction and the motivation for these research areas. It is composed of a brief review of the history and the future of modern computers and the state-of-art areas in quantum computation and information. Chapter 2 will be dedicated to introducing the concept of entanglement, its importance, quantification and applications. Then in Chapter 3, the properties of a set of localized spins, which are coupled to an external magnetic field through exchange interaction, are investigated. It is shown that entanglement can be controlled and tuned by varying the anisotropy parameter in the Hamiltonian, and by introducing impurities into the systems. Furthermore, the scheme for amplifying the internal entanglement by external interaction is also studied. In Chapter 4, the applications of the entanglement concept for de-coherence and dynamics is considered. In particular, the dynamics of entanglement for one-dimensional spin systems, which are coupled through nearest neighbor exchange interaction and subject to an external time-dependent magnetic field, is investigated. Using the two-site density matrix, the time-dependent entanglement of formation between nearest neighbor qubits is calculated. It is found that the entanglement can be localized between nearest neighbor qubits for certain values of the external time-dependent magnetic field. In quantum chemistry calculations, the correlation energy is defined as the difference between the Hartree-Fock limit energy and the exact solution of the non-relativistic Schrödinger equation. In Chapter 5, the application of entanglement as an alternative measure of the electron correlation in quantum chemistry calculations is proposed. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics. Finally, Chapter 6 presents the latest research results in developing quantum algorithms for searching the global minima. In this Chapter, the modified Grover’s quantum algorithm using modest numbers of quantum bits to find a global minimum for real problems is demonstrated.
An antiferromagnetically exchange-coupled dimer of single molecule magnets which possesses a large spin tunneling has been investigated. For this system, the ground and first excited states are entangled states, and the Hamiltonian is effectively similar to that of a two-state system at 2sth order in perturbation theory; thus this system can be mapped to an entangled pseudospin 1/2 particles. We study the effects of interaction and rotation of this system about its staggered easy-axis direction. The corresponding Hamiltonian of a rotated two-state entangled spin system is derived with its exact low-energy eigenstates and eigenvalues. We briefly discuss the effect of a dissipative environment on this rotated two-state system.