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Springer eBooks

Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

Paola Cappellaro

Published Aug 21, 2013• 10 citations
Publisher
DOI
10.1007/978-3-642-39937-4_6

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Quantum communication through spin chains has been extensively investigated. In this scenario, state transfer through linearly arranged spins connected by uniform nearest-neighbor couplings qualifies as a natural choice, with minimal control requirements. However, quantum states usually cannot be perfectly transferred through a uniformly coupled chain due to the dispersion of the chain. Here, we propose an effective quantum control technique to realize almost exact state transfer (AEST) in a quantum spin chain. The strategy is to add a leakage elimination operator Hamiltonian to the evolution, which implements a sequence of pulse control acting on a perfect state transfer subspace. By using the one-component Feshbach PQ partitioning technique, we obtain the conditions over the required pulses. AEST through a spin chain can then be obtained under a suitable pulse intensity and duration.
We propose a method for quantum state transfer in spin chains using an adiabatic passage technique. Modifying even and odd nearest-neighbour couplings in time allows transfer fidelities arbitrarily close to one to be achieved, without the need for precise control of coupling strengths and timing. We study in detail transfer by adiabatic passage in a spin-1 chain governed by a generalized Heisenberg Hamiltonian. We consider optimization of the transfer process applying optimal control techniques. We discuss a realistic experimental implementation using cold atomic gases confined in deep optical lattices.
The coherent transport of quantum states between distant qubits is one of the key milestones towards the realisation of large-scale quantum computers [1]. For static qubits, this state transfer is often envisioned to be carried out only by the internal dynamics of the system, which has the great advantage that detrimental influences of the environment are minimised. A chain of spin-1/2-qubits with ferromagnetic coupling has been suggested as an implementation of a coherent transport which is perfect in theory [2]. In this scheme, a precise engineering of the coupling strengths between adjacent spins is crucial. To date, such a quantum state transfer has only been achieved for the modest system size of three qubits, employing nuclear magnetic resonance [3]. However, this concept is by no means restricted to spin chains; it is therefore possible to resort to another physical platform, such as optics, to investigate the capabilities of the transferring Hamiltonian.