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Physical Review A

Almost-exact state transfer by leakage-elimination-operator control in a non-Markovian environment

Zhao-Ming Wang, Feng-Hua Ren, Da-Wei Luo, Zhan-Yuan Yan, Lian-Ao Wu

Published Oct 20, 2020• 30 citations
Publisher

Abstract

We investigate the feasibility of using an effective pulse control method to realize an almost exact state transmission through a uniform chain where the communication channel is immersed in a quantum environment. This pulse control is treated in a nonperturbative fashion, allowing for a more precise view. Using the non-Markovian quantum state diffusion equation, we calculate the dynamics of the transmission fidelity. The results show that the memory effects of the environment can support an effective transmission control that can be boosted under a non-Markovian environment. Our scheme provides another way to realize almost exact state transmission in a spin chain system.

DOI
10.1103/physreva.102.042406

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We investigate the feasibility of using an effective pulse control method to realize an almost exact state transmission through a uniform chain where the communication channel is immersed in a quantum environment. This pulse control is treated in a nonperturbative fashion, allowing for a more precise view. Using the non-Markovian quantum state diffusion equation, we calculate the dynamics of the transmission fidelity. The results show that the memory effects of the environment can support an effective transmission control that can be boosted under a non-Markovian environment. Our scheme provides another way to realize almost exact state transmission in a spin chain system.
Abstract Transmission of a quantum state is essential for performing quantum information processing tasks. The communication channel will be inevitably immersed in its surrounding environment under realistic conditions. In this paper, we investigate the influence of environment noise on the transmission fidelity when transferring a quantum state through a spin chain. The non-Markovian open system dynamics is systematically analyzed by using the quantum state diffusion equation method. With each spin immersed in its own finite temperature and non-Markovian heat bath, we consider three types of system–bath interaction: dephasing, dissipation and spin-boson. The transmission fidelity is found to decrease with the increasing bath temperature and system–bath coupling strength. Interestingly, we find that the bath non-Markovianity can help enhancing the transmission fidelity.
We investigate the influence of environment noise on the control cost and the quantum speed limit time (QSLT) in the process of almost-exact state transmission (AEST) through a spin chain under pulse control. The chain is immersed in its surrounding non-Markovian, finite-temperature heat baths. We find that AEST can be realized in weak system-bath coupling, low temperature, and strong non-Markovian baths under effective external control. Correspondingly, the control cost and QSLT increase with increasing bath temperature and coupling strength. It is noticeable that non-Markovianity from the baths can be helpful to reduce the control cost and shorten the QSLT. Furthermore, we find that there exists a trade-off between the control cost and transmission fidelity and that higher fidelity requires higher cost. In addition, the minimum control cost has been found to obtain certain transmission fidelity.
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 consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.
Adiabatic quantum computation requires that the system remains in its ground state. However, an adiabatic process often loses partly or entirely its quantumness, such as entanglement in its long runtime, due to the system-environment interactions. Here we put forward an effective quantum control technique to realize the adiabatic quantum search algorithm in a nonadiabatic regime and in the presence of environment. Using the non-Markovian quantum state diffusion equation approach, we numerically study the system dynamics characterized by the success probability. The results show that the probability increases with decreasing coupling strength and temperature. In particular, non-Markovianity from the environment can help to enhance the success probability. By choosing a suitable pulse intensity and period, a high success probability can be obtained in a short runtime for weak system-bath coupling, low temperature, and strong non-Markovian heat baths.
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.