arXiv quant-ph/05122092005-12-22quant-phcond-mat.other

量子计算、复杂性和多体物理学

Quantum Computation, Complexity, and Many-Body Physics

Rolando D. Somma

备注：: PhD Thesis; Figures compressed; If needed, contact the author for a version in spanish. (Full abstract is in the thesis file)

摘要：

最近开发的量子算法表明，量子计算机可以比传统计算机更有效地解决某些问题并执行某些任务。除其他原因外，这是由于可能产生非经典关联，或量子纠缠，这是一种很难或不可能通过经典信息方法再现的现象。在这篇论文中，我首先研究在由二能级量子元或量子比特构成的量子计算机上模拟量子系统。为此，我提出了代数映射，允许一个获得的物理性质和计算关联函数的费米子，任意子，玻色子系统与这样的计算机。结果表明，制备包含计算所需信息的量子态的复杂性是至关重要的。其次，我提出了一个广泛的量子计算，其中可能涉及纠缠态，可以在两种类型的计算机上以相同的效率进行模拟。广义量子纠缠的概念自然就出现了。这种对纠缠的概括是基于这样一种想法，即纠缠是一个依赖于粒子的概念，也就是说，相对于一组优选的可观测量。

英文摘要：

Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating non-classical correlations, or quantum entanglement, which is a phenomena hard or impossible to reproduce by classical-information methods. In this thesis I first investigate the simulation of quantum systems on a quantum computer constructed of two-level quantum elements or qubits. For this purpose, I present algebra mappings that allow one to obtain physical properties and compute correlation functions of fermionic, anyonic, and bosonic systems with such a computer. The results obtained show that the complexity of preparing a quantum state which contains the desired information for the computation is crucial. Second, I present a wide class of quantum computations, which could involve entangled states, that can be simulated with the same efficiency on both types of computers. The notion of generalized quantum entanglement then naturally emerges. This generalization of entanglement is based on the idea that entanglement is an observer-dependent concept, that is, relative to a set of preferred observables.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文