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Journal of Applied Physics

Quantum gates controlled by spin chain soliton excitations

Alessandro Cuccoli, Davide Nuzzi, Ruggero Vaia, Paola Verrucchi

Published Jan 10, 2014• 6 citations
Publisher

Abstract

Propagation of soliton-like excitations along spin chains has been proposed as a possible way for transmitting both classical and quantum information between two distant parties with negligible dispersion and dissipation. In this work, a somewhat different use of solitons is considered. Solitons propagating along a spin chain realize an effective magnetic field, well localized in space and time, which can be exploited as a means to manipulate the state of an external spin (i.e., a qubit) that is weakly coupled to the chain. We have investigated different couplings between the qubit and the chain, as well as different soliton shapes, according to a Heisenberg chain model. It is found that symmetry properties strongly affect the effectiveness of the proposed scheme, and the most suitable setups for implementing single qubit quantum gates are singled out.

DOI
10.1063/1.4857575

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Abstract Solitons provide a promising means to control the state of a spin-qubit in quantum information technology. In this paper, we consider the anisotropic interaction between a soliton, propagating in a ferromagnetic Heisenberg spin chain and a spin- <?CDATA $\frac{1}{2}$?> 1 2 particle (qubit). The spin chain exhibits an on-site anisotropy and spin-spin nearest-neighbor and next-nearest-neighbor interactions. The Bloch sphere picture is employed to investigate the spin- <?CDATA $\frac{1}{2}$?> 1 2 dynamics. We found that increasing the anisotropic and the second neighbor interactions leads to an increase of the deviation of the spin- <?CDATA $\frac{1}{2}$?> 1 2 particle from its initial state.

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Propagation of soliton-like excitations along spin chains has been proposed as a possible way for transmitting both classical and quantum information between two distant parties with negligible dispersion and dissipation. In this work, a somewhat different use of solitons is considered. Solitons propagating along a spin chain realize an effective magnetic field, well localized in space and time, which can be exploited as a means to manipulate the state of an external spin (i.e., a qubit) that is weakly coupled to the chain. We have investigated different couplings between the qubit and the chain, as well as different soliton shapes, according to a Heisenberg chain model. It is found that symmetry properties strongly affect the effectiveness of the proposed scheme, and the most suitable setups for implementing single qubit quantum gates are singled out.
Many proposals for quantum devices are based on qubits that are physically realized by the spin magnetic moment of some quantum object. In this case, one of the most often adopted strategies for manipulating qubits is that of using external magnetic fields. However, selectively applying a field just to one qubit may be a practically unattainable goal, as it is, for instance, in most solid-state based setups. In this work, we present a proposal for using nonlinear excitations of solitonic type to accomplish the above task. Our scheme entails the generation of a dynamical soliton in a classical spin-chain which is locally coupled with one qubit: as the soliton runs through, the qubit behaves, due to its interaction with the chain, as if it were subject to a magnetic field with a time dependence that follows from the soliton's features. We here present results for the time evolution of the qubit density-matrix induced by the overall dynamics of the above scheme.
We propose a method for acting on the spin state of a spin- localized particle, or qubit , by means of a magnetic signal effectively generated by the nearby transit of a magnetic soliton, there conveyed through a transmission line. We first introduce the specific magnetic soliton of which we will make use, and briefly review the properties that make it apt to represent a signal. We then show that a Heisenberg spin chain can serve as transmission line, and propose a method for injecting a soliton into the chain by acting just on one of its ends. We finally demonstrate that the resulting magnetic pulse can indeed cause, just passing by the spin- localized particle embodying the qubit, a permanent change in its spin state, thus realizing the possibility of getting through to a single, localized qubit, and manipulating its state. A thorough analysis of how the overall dynamical system operates depending on the setting of its parameters demonstrates that fine tuning is not necessary as there exists an extended region in the parameters space that corresponds to effective functioning. Moreover, we show that possible noise on the transmission line does not invalidate the scheme.
We study the low energy states of one-dimensional spin chain clusters consisting of three spin-1/2 Heisenberg particles. When applying an external magnetic field on the spin chain cluster, the ground state doublet will generate Zeeman splitting. As a two-level quantum system, the split ground state doublet can be defined as a new 'spin cluster qubit'. The cluster quibit is shown to be more robust with a smaller decoherence rate. We realize universal single-qubit gates with the algebraic dynamical method, by applying a time-dependent magnetic field on the spin cluster. We also investigate a two-qubit system made up of two such Heisenberg spin chain clusters which interact through a tunable Heisenberg coupling. In the two-qubit product basis, the controlled quantum phase gates can be generated by applying a magnetic field along the z-axis on the system of the two clusters. One can realize the controlled-NOT gate through a three-step time evolution by adjusting the corresponding physical parameters. Our scheme involves two kinds of dynamically distinct operations, which is much simpler and more feasible.
We demonstrate that nonlinear magnetic solitary excitations (solitons) traveling through a Heisenberg spin chain may be used as a robust tool capable of coherent control of the qubit's state. The physical problem is described by a Hamiltonian involving the interaction between the soliton and the qubit. We show that under certain conditions the generic Hamiltonian may be mapped on that of a qubit two-level system with matrix elements depending on the soliton parameters. We considered the action of a bright and a dark soliton depending on the driving nonlinear wave function. We considered a local interaction restricted the closest to the qubit spin in the chain. We computed the expressions of the physical quantities of interest for all cases and analyzed their behavior in some special limits.
Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements.
Abstract Solitons provide a promising means to control the state of a spin-qubit in quantum information technology. In this paper, we consider the anisotropic interaction between a soliton, propagating in a ferromagnetic Heisenberg spin chain and a spin- <?CDATA 12\frac{1}{2}21​?> 1 2 particle (qubit). The spin chain exhibits an on-site anisotropy and spin-spin nearest-neighbor and next-nearest-neighbor interactions. The Bloch sphere picture is employed to investigate the spin- <?CDATA 12\frac{1}{2}21​?> 1 2 dynamics. We found that increasing the anisotropic and the second neighbor interactions leads to an increase of the deviation of the spin- <?CDATA 12\frac{1}{2}21​?> 1 2 particle from its initial state.