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arXiv:2111.14644

Transforming spin chains with a continuous driving field

Hudaiba Soomro, Adam Zaman Chaudhry

Published Nov 29, 2021• 0 citations
arXivHTMLPDF

Abstract

A continuous, sinusoidal control field is used to suitably transform quantum spin chains. In particular, we are able to transform the quantum Ising chain to the quantum XY model, and the XY model to the XYZ spin chain. Our applied control field can also mitigate the effect of noise on the spin chain. We show how these spin chain transformations can be useful for quantum state transfer as well as entanglement generation.

DOI
10.48550/arxiv.2111.14644

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A continuous, sinusoidal control field is used to suitably transform quantum spin chains. In particular, we are able to transform the quantum Ising chain to the quantum XY model, and the XY model to the XYZ spin chain. Our applied control field can also mitigate the effect of noise on the spin chain. We show how these spin chain transformations can be useful for quantum state transfer as well as entanglement generation.
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For spins chains to be useful for quantum information processing tasks, the interaction between the spin chain and its environment generally needs to be suppressed. In this paper, we propose the use of strong static and oscillating control fields in order to effectively remove the spin-chain-environment interaction. We find that our control fields can also effectively transform the spin-chain Hamiltonian. In particular, interaction terms which are absent in the original spin-chain Hamiltonian appear in the time-averaged effective Hamiltonian once the control fields are applied, implying that spin-spin interactions can be engineered via the application of static and oscillating control fields. This transformation of the spin chain can then potentially be used to improve the performance of the spin chain for quantum information processing tasks. For example, our control fields can be used to achieve almost perfect quantum state transfer across a spin chain even in the presence of noise. As another example, we show how the use of particular static and oscillating control fields not only suppresses the effect of the environment, but can also improve the generation of two-spin entanglement in the spin chain.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.
We propose a protocol restoring the state transferred along the spin chain governed by the XY-Hamiltonian. Such dynamics does not preserve the excitation number and leads to mixing multiple-quantum coherence matrices of orders having the same parities. Depending on the initial state, this results in generating either all possible or only even-order multiple-quantum coherence matrices. Restoring is established via the special unitary transformation applied to the receiver side of the chain (extended receiver). An example of restoring [Formula: see text]- and [Formula: see text]-order coherence matrices in two-qubit state transfer is considered. Entanglement transfer in such process is also studied and possibility of its amplification is demonstrated.
We propose a setup, based on a periodically driven spin chain, that can realize a high-quality quantum router. We present two protocols, which utilize this setup, that can either generate highly entangled two-qubit states over an arbitrary distance or transfer single-qubit states with high fidelity to any desired location on the chain. In addition, we can execute several protocols at the same time and also store quantum states on the spin chain. Our protocols exploit the effect of coherent destruction of tunneling to control, which spins on the chain couple to each other. This control is acquired by suitably shaping the external driving field. The success of our protocols does not depend on the values of the couplings between the spins as long as they are finite and much smaller than the driving frequency. Our setup is scalable, robust against errors, and may be of practical use for future quantum information technologies.
We demonstrate that a translation-invariant chain of interacting quantum systems can be used for high efficiency transfer of quantum entanglement and the generation of multiparticle entanglement over large distances and between arbitrary sites without the requirement of precise spatial or temporal control. The scheme is largely insensitive to disorder and random coupling strengths in the chain. We discuss harmonic oscillator systems both in the case of arbitrary Gaussian states and in situations when at most one excitation is in the system. The latter case, which we prove to be equivalent to an xy -spin chain, may be used to generate genuine multiparticle entanglement. Such a 'quantum data bus' may prove useful in future solid state architectures for quantum information processing.