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arXiv:quant-ph/0702265 · Physical Review A

Controlled quantum-state transfer in a spin chain

Jiangbin Gong, Paul W. Brumer

Published Mar 23, 2007• 30 citations
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Abstract

Control of the transfer of quantum information encoded in quantum wave packets moving along a spin chain is demonstrated. Specifically, based on a relationship with control in a paradigm of quantum chaos, it is shown that wave packets with slow dispersion can automatically emerge from a class of initial superposition states involving only a few spins, and that arbitrary unspecified traveling wave packets can be nondestructively stopped and later relaunched with perfection. The results establish an interesting application of quantum chaos studies in quantum information science.

DOI
10.1103/physreva.75.032331

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Control of the transfer of quantum information encoded in quantum wave packets moving along a spin chain is demonstrated. Specifically, based on a relationship with control in a paradigm of quantum chaos, it is shown that wave packets with slow dispersion can automatically emerge from a class of initial superposition states involving only a few spins, and that arbitrary unspecified traveling wave packets can be nondestructively stopped and later relaunched with perfection. The results establish an interesting application of quantum chaos studies in quantum information science.
We demonstrate that perfect state transfer can be achieved using an engineered spin chain and clean local end-chain operations, without requiring the initialization of the state of the medium nor fine-tuning of control pulses. This considerably relaxes the prerequisites for obtaining reliable transfer of quantum information across interacting-spin systems. Moreover, it allows us to shed light on the interplay among purity, entanglement, and operations on a class of many-body systems potentially useful for quantum information processing tasks.
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.
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.
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 radically different and generally applicable approach to efficient control of dynamics in spin chains of arbitrary length. The approach relies on the creation of localized spin waves, ``spin solitons'', and efficient propagation of these soliton states through the spin chain. The methods presented are expected to find immediate applications in control of spin dynamics in coherent spectroscopy and quantum information processing.
Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum signal amplification in a one-dimensional spin-chain model. It is shown that, by adiabatically moving an external field applied to a spin chain that is also irradiated with a transverse driving field, a robust spin amplifier may be realized with little dispersion. Our results may find applications in spin-based quantum-information processing and in controlled growth of ``Schr\"odinger cat'' states.
One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as ℏ→0.