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arXiv:1505.04862 · Physical Review A

Robust state transfer with high fidelity in spin-1/2 chains by Lyapunov control

Zhengang Shi, Xiaolong Zhao, X. X. Yi

Published Mar 5, 2015• 35 citations
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Abstract

Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at nonstationary state (or information) transfer from the first spin to the end spin at a fixed time. The present scheme possesses the following advantages. First, the scheme does not require precise manipulations of the control time. Second, it is robust against uncertainties in the initial states and fluctuations in the control fields. Third, the controls are exerted only on the boundary sites of the chain. It works for variable spin-1/2 chains with different periodic structures and has good scalability. The feasibility to replace the control fields by square pules is explored, which simplifies the realization in experiments.

DOI
10.1103/physreva.91.032301

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Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at nonstationary state (or information) transfer from the first spin to the end spin at a fixed time. The present scheme possesses the following advantages. First, the scheme does not require precise manipulations of the control time. Second, it is robust against uncertainties in the initial states and fluctuations in the control fields. Third, the controls are exerted only on the boundary sites of the chain. It works for variable spin-1/2 chains with different periodic structures and has good scalability. The feasibility to replace the control fields by square pules is explored, which simplifies the realization in experiments.
Spin chains have been widely studied as quantum channels for short-distance communication in quantum devices, where many-body dynamics can mediate quantum-state transfer between distant sites. In finite unmodulated chains, however, dispersion and interference effects associated with the static Hamiltonian often limit the achievable transfer fidelity. Here we investigate the transfer of single-qubit and Bell states in finite XXXXXX spin chains under periodic switching between two Hamiltonians with different boundary couplings. Inspired by Parrondo's paradox, we examine whether alternating between two configurations that individually yield suboptimal transfer fidelities can generate enhanced coherent transmission. Using Floquet theory together with numerical simulations in the single-excitation subspace, we show that periodic driving can outperform static configurations and achieve higher transfer fidelities. This enhancement originates from the noncommutativity of the driven Hamiltonians and reflects a purely coherent interference effect. We further analyze the dependence of the protocol on system size and driving parameters and examine its robustness to asymmetric boundary couplings. Our results show that the transfer fidelity remains stable under moderate disorder, indicating that simple time-dependent control of boundary couplings provides an effective strategy to enhance quantum-state transfer in spin-chain communication channels and optimize quantum information processing in engineered many-body systems.
Abstract Quantum state transfer (QST) plays a central role in the field of quantum computation and communication, but its quality will be deteriorated by the ubiquitous variations and noise in quantum systems. Here we propose robust and nonadiabatic protocols for transmitting quantum state across a strongly coupled spin chain, especially in the presence of unwanted disorders in the couplings. To this end, we approximately map the low-energy subspaces of the odd-size Heisenberg chain to a two-level system, and derive the sensitivity of the final fidelity with respect to systematic deviations or time-varying fluctuations. Subsequently, leveraging the flexibility of the inverse-engineering technique, we optimize the state-transfer robustness concerning these perturbations individually. The resulting schemes allow for more stable QST than the original accelerated schemes and only require manipulating the two boundary couplings instead of the whole system, which open up the possibility of fast and robust information transfer in spin-based quantum systems.
We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.
We present several protocols for reliable quantum state transfer through an XY spin chain. Among these is a simple two-spin encoding that achieves a remarkably high-fidelity transfer for an arbitrary quantum state. The fidelity of the transfer also decreases slowly with increasing chain length. Furthermore, the reliability can be increased by taking advantage of a local memory and/or confirming transfer using a second spin chain. The simplicity and high fidelity of the encoding makes this a candidate for near-future experiments including a test of the quantum speed limit.
The spin chain is a system that has been widely studied for its quantum phase transition. It also holds potential for practical application in quantum information, including quantum communication and quantum computation. In this paper, we propose a scheme for conditional state transfer in a Heisenberg XXZ spin chain. In our scheme, the absence or presence of a periodic driving potential results in either a perfect state transfer between the input and output ports, or a complete blockade at the input port. This scheme is formalized by deriving an analytical expression of the effective Hamiltonian for the spin chain subject to a periodic driving field in the high-frequency limit. The influence of the derivation of the optimal parameter on the performance of the state transfer is also examined, showing the robustness of the spin chain for state transfer. In addition, the collective decoherence effect on the fidelity of state transfer is discussed. The proposed scheme paves the way for the realization of integrated quantum logic elements, and may find application in quantum information processing.