计算交换代数2

计算交换代数将要成为这个世纪应用到现实世界的最为重要的数学工具之一，随着当今计算技术的飞速发展，采用符号计算的方法处理工业尺度的问题已经成为现实。本书的主要目的是继续为这种发展趋势提供理论基础，深入其中将可以发现与现世界相关的很多线索和暗示。虽然数值方法至今依然占据着统治地位，符号方法被视作数值方法的补充；虽然少数计算机代数系统（包括CoCoA）提供了进行混合计算的可能（例如混合了数值和符号方法），     

Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.