Joachim Stolze

Spin chains as perfect quantum state mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics, any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at an arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.

Robustness of spin-coupling distributions for perfect quantum state transfer

The transmission of quantum information between different parts of a quantum computer is of fundamental importance. Spin chains have been proposed as quantum channels for transferring information. Different configurations for the spin couplings were proposed in order to optimize the transfer. As imperfections in the creation of these specific spin-coupling distributions can never be completely avoided, it is important to find out which systems are optimally suited for information transfer by assessing their robustness against imperfections or disturbances. We analyze different spin coupling distributions of spin chain channels designed for perfect quantum state transfer. In particular, we study the transfer of an initial state from one end of the chain to the other end. We quantify the robustness of different coupling distributions against perturbations and we relate it to the properties of the energy eigenstates and eigenvalues. We find that the localization properties of the systems play an important role for robust quantum state transfer.

Exact dynamics in the inhomogeneous central-spin model

We study the dynamics of a single spin

Spin chains for robust state transfer: Modified boundary couplings versus completely engineered chains

1∕2

Impurity spin relaxation inS=12XXchains

coupled to a bath of spins

Impurity spin relaxation in S=1/2 XX chains

1∕2

Ground states of extended Hubbard models in the atomic limit

by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins

Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains

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Robustness of Spin-Chain State-Transfer Schemes

, the oscillation frequency is proportional to

PERFECT STATE TRANSFER IN XX CHAINS INDUCED BY BOUNDARY MAGNETIC FIELDS

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