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arXiv:1609.01397 · Quantum

Tailoring spin chain dynamics for fractional revivals

Alastair Kay

Published Aug 10, 2017• 9 citations
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Abstract

The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites. We concentrate in particular on cases where the excitation is superposed over a small subset of the qubits on the spin chain, known as fractional revivals, demonstrating that spin chains are capable of producing a far greater range of fractional revivals than previously known, at high speed. We also provide a numerical technique for generating chains that produce arbitrary single-excitation states, such as the W state.

DOI
10.22331/q-2017-08-10-24

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The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites. We concentrate in particular on cases where the excitation is superposed over a small subset of the qubits on the spin chain, known as fractional revivals, demonstrating that spin chains are capable of producing a far greater range of fractional revivals than previously known, at high speed. We also provide a numerical technique for generating chains that produce arbitrary single-excitation states, such as the W state.
We design a quasi-one-dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left-hand site to any specified single-particle state on the whole chain. Our treatment is an exact solution to a problem which has already been addressed in approximate ways. As two important examples, we study the WWW states and Gaussian states of arbitrary width.
In this thesis, we discuss the natural dynamics of spin chains with regards to their potential role as information carriers in quantum computers and also standalone uses in a quantum computational context. We discuss a range of spin chain devices, expanding existing results on linear chains and simple branched devices to more complex geometries and circular devices. Over the course of this work, we analyse requirements and feasibility of perfect state transfer using the natural dynamics of spin chains and present an extensive investigation into the effects of a number of perturbations on the dynamics of these devices. This includes both fabrication defects and other sources of perturbations. We also present other potential uses of spin chains, including state storage, and introduce an original protocol for the generation of cluster state ladders using only a single linear spin chain.
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.
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.