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Chinese Journal of Quantum Electronics

Perfect information transfer in spin chains and perfect state control in quantum chains

Xin Chen, Junhui Shi

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Based on analysis of neighbor-coupled spin chains,a method to get the parameters of the spin chains for perfect information transfer is given,and all analytical solutions are obtained by using Groebner basis analysis.The method is suitable to get the parameters of pulse-driven perfect state control in multilevel chains.The results can be used to analyze structures of the solutions or find particular parameters with optimal properties.

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Based on analysis of neighbor-coupled spin chains,a method to get the parameters of the spin chains for perfect information transfer is given,and all analytical solutions are obtained by using Groebner basis analysis.The method is suitable to get the parameters of pulse-driven perfect state control in multilevel chains.The results can be used to analyze structures of the solutions or find particular parameters with optimal properties.
The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscillations from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Gröbner basis analysis technique is used to generalize the results and get all analytical solutions for perfect population transfer. Explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.
We investigate quantum state transfer in XY\mathit{XY}XY spin chains and propose a recursive procedure to construct the nonuniform couplings within these chains of arbitrary length in order to achieve perfect state transfer. We show that this method is capable of finding all possible coupling schemes for perfect state transfer. These schemes, without external control fields, involve analytically identified engineered couplings without the need for dynamical control. The analytical solutions provide all information for coupling design.
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.
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.
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.
In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an inverse eigenvalue problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.