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arXiv:1101.4509 · Journal of Physics Conference Series

Long-range interactions and information transfer in spin chains

Rebecca Ronke, Tim Spilled, Irene D’Amico

Published Mar 1, 2011• 8 citations
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Abstract

One of the main proposed tools to transfer information in a quantum computational context are spin chains. While spin chains have shown to be convenient and reliable, it has to be expected that, as with any implementation of a physical system, they will be subject to various errors and perturbative factors. In this work we consider the transfer of entangled as well as unentangled states to investigate the effects of various errors, paying particular attention to unwanted long-range interactions.

DOI
10.1088/1742-6596/286/1/012020

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One of the main proposed tools to transfer information in a quantum computational context are spin chains. While spin chains have shown to be convenient and reliable, it has to be expected that, as with any implementation of a physical system, they will be subject to various errors and perturbative factors. In this work we consider the transfer of entangled as well as unentangled states to investigate the effects of various errors, paying particular attention to unwanted long-range interactions.
Spin chains have been proposed as a reliable and convenient way of transferring information and entanglement in a quantum computational context. Nonetheless, it has to be expected that any physical implementation of these systems will be subject to several perturbative factors which could potentially diminish the transfer quality. In this paper, we investigate a number of possible fabrication defects in the spin chains themselves as well as the effect of nonsynchronous or imperfect input operations, with a focus on the case of multiple excitation and qubit transfer. We consider both entangled and unentangled states and, in particular, the transfer of an entangled pair of adjacent spins at one end of a chain under the mirroring rule and also the creation of entanglement resulting from injection at both end spins.
The spin chain is a theoretical work-horse of the physicist, providing a convenient, tractable model that yields insight into a host of physical phenomena including conduction, frustration, superconductivity, topological phases, localisation, phase transitions, quantum chaos and even string theory. Our ultimate aim, however, is not just to understand the properties of a physical system, but to harness it for our own ends. We therefore study the possibilities for engineering a special class of spin chain, envisaging the potential for this to feedback into the original physical systems. We pay particular attention to the generation of multipartite entangled states such as the W (Dicke) state, superposed over multiple sites of the chain.
Creation of entanglement is considered theoretically and numerically in an ensemble of spin chains with dipole-dipole interaction between the spins. The unwanted effect of the long-range dipole interaction is compensated by the optimal choice of the parameters of radio-frequency pulses implementing the protocol. The errors caused by (i) the influence of the environment, (ii) nonselective excitations, (iii) influence of different spin chains on each other, (iv) displacements of qubits from their perfect locations, and (v) fluctuations of the external magnetic field are estimated analytically and calculated numerically. For the perfectly entangled state the zzz component MMM of the magnetization of the whole system is equal to zero. The errors lead to a finite value of MMM. If the number of qubits in the system is large, MMM can be detected experimentally. Using the fact that MMM depends differently on the parameters of the system for each kind of error, varying these parameters would allow one to experimentally determine the most significant source of errors and to optimize correspondingly the quantum computer design in order to decrease the errors and $\ensuremath{\mid}M\ensuremath{\mid}$. Using our approach one can benchmark the quantum computer, decrease the errors, and prepare the quantum computer for implementation of more complex quantum algorithms.
Abstract Spin chains have long been considered an effective medium for long-range interactions, entanglement generation, and quantum state transfer. In this work, we explore the properties of a spin chain implemented with superconducting flux circuits, designed to act as a connectivity medium between two superconducting qubits. The susceptibility of the chain is probed and shown to support long-range, cross-chain correlations. In addition, interactions between the two end qubits, mediated by the coupler chain, are demonstrated. This work has direct applicability in near term quantum annealing processors as a means of generating long-range, coherent coupling between qubits.