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This thesis explores the use of entangled states in quantum computation andquantum information science. Entanglement, a quantum phenomenon with noclassical counterpart, has been identified as an important and quantifiableresource in many areas of theoretical quantum information science, includingquantum error correction, quantum cryptography, and quantum algorithms. Wefirst investigate the equivalence classes of a particular class of entangledstates (known as graph states due to their association with mathematicalgraphs) under local operations. We prove that for graph states corresponding tographs with neither cycles of length 3 nor 4, the equivalence classes can becharacterized in a very simple way. We also present software for analyzing andmanipulating graph states. We then study quantum error-correcting codes whosecodewords are highly entangled states. An important area of investigationconcerning QECCs is to determine which resources are necessary in order tocarry out any computation on the code to an arbitrary degree of accuracy, whilesimultaneously maintaining a high degree of resistance to noise. We prove thattransversal gates, which are designed to prevent the propagation of errorsthrough a system, are insufficient to achieve universal computation on almostall QECCs. Finally, we study the problem of creating efficient quantum circuitsfor creating entangling measurements. Entangling measurements can be used toharness the apparent extra computing power of quantum systems by allowing us toextract information about the global, collective properties of a quantum stateusing local measurements. We construct explicit quantum circuits that createentangling measurements, and show that these circuits scale polynomially in theinput parameters.

The Study of Entangled States in Quantum Computation and Quantum Information Science