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arXiv:2005.01311 · Physical Review A

Almost exact state transfer in a spin chain via pulse control

Zhao-Ming Wang, M. S. Sarandy, Lian-Ao Wu

Published Aug 3, 2020• 19 citations
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Abstract

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.

DOI
10.1103/physreva.102.022601

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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 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.
Traditional many-body teleportation relies on the strong interaction property of a quantum many-body system, which usually requires numerous qubits and entanglement resources, making it difficult to realize experimentally. A natural scheme is to use a 1D spin chain with simple structure to realize many-body teleportation. In this paper, we analyze the conditions for general quantum many-body teleportation and construct an effective control Hamiltonian, realizing quantum many-body teleportation on the controlled 1D spin chain. Our scheme, which only requires forward evolution and local measurements, can be used to perform quantum state transfer without the special presetting and modulation of coupling parameters of the chain and without strict control over the evolution time, thereby enhancing the experimental realizability. Furthermore, we improve the efficiency and accuracy of quantum state transfer by introducing quantum optimal control (QOC) technique to optimize the control pulse sequences.
We show that an effective two-qubit gate can be obtained from the free evolution of three spins in a chain with nearest neighbor XY coupling, without local manipulations. This gate acts on the two remote spins and leaves the mediating spin unchanged. It can be used to perfectly transfer an arbitrary quantum state from the first spin to the last spin or to simultaneously communicate one classical bit in each direction. One ebit can be generated in half of the time for state transfer. For longer spin chains, we present methods to create or transfer entanglement between the two end spins in half of the time required for quantum state transfer, given tunable coupling strength and local magnetic field. We also examine imperfect state transfer through a homogeneous XY chain.
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.
We present an introductory overview of the use of spin chains as quantum wires, which has recently developed into a topic of lively interest. The principal motivation is in connecting quantum registers without resorting to optics. A spin chain is a permanently coupled 1D system of spins. When one places a quantum state on one end of it, the state will be dynamically transmitted to the other end with some efficiency if the spins are coupled by an exchange interaction. No external modulations or measurements on the body of the chain, except perhaps at the very ends, is required for this purpose. For the simplest (uniformly coupled) chain and the simplest encoding (single qubit encoding), however, dispersion reduces the quality of transfer. We present a variety of alternatives proposed by various groups to achieve perfect quantum state transfer through spin chains. We conclude with a brief discussion of the various directions in which the topic is developing.