dorsal/arxiv
View SchemaEntanglement, quantum phase transitions and quantum algorithms
| Authors | Roman Orus |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608013 |
| URL | https://arxiv.org/abs/quant-ph/0608013 |
Abstract
The work that we present in this thesis tries to be at the crossover of quantum information science, quantum many-body physics, and quantum field theory. We use tools from these three fields to analyze problems that arise in the interdisciplinary intersection. More concretely, in Chapter 1 we consider the irreversibility of renormalization group flows from a quantum information perspective by using majorization theory and conformal field theory. In Chapter 2 we compute the entanglement of a single copy of a bipartite quantum system for a variety of models by using techniques from conformal field theory and Toeplitz matrices. The entanglement entropy of the so-called Lipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with that of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of scaling of quantum correlations in quantum phase transitions to the study of quantum algorithms, focusing on Shor's factorization algorithm and quantum algorithms by adiabatic evolution solving an NP-complete and the searching problems. Also, in Chapter 5 we use techniques originally inspired by condensed-matter physics to develop classical simulations, using the so-called matrix product states, of an adiabatic quantum algorithm. Finally, in Chapter 6 we consider the behavior of some families of quantum algorithms from the perspective of majorization theory. The structure within each Chapter is such that the last section always summarizes the basic results. Some general conclusions and possible future directions are briefly discussed in Chapter 7. Appendix A, Appendix B and Appendix C respectively deal with some basic notions on majorization theory, conformal field theory, and classical complexity theory.
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"abstract": "The work that we present in this thesis tries to be at the crossover of\nquantum information science, quantum many-body physics, and quantum field\ntheory. We use tools from these three fields to analyze problems that arise in\nthe interdisciplinary intersection. More concretely, in Chapter 1 we consider\nthe irreversibility of renormalization group flows from a quantum information\nperspective by using majorization theory and conformal field theory. In Chapter\n2 we compute the entanglement of a single copy of a bipartite quantum system\nfor a variety of models by using techniques from conformal field theory and\nToeplitz matrices. The entanglement entropy of the so-called\nLipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with\nthat of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of\nscaling of quantum correlations in quantum phase transitions to the study of\nquantum algorithms, focusing on Shor\u0027s factorization algorithm and quantum\nalgorithms by adiabatic evolution solving an NP-complete and the searching\nproblems. Also, in Chapter 5 we use techniques originally inspired by\ncondensed-matter physics to develop classical simulations, using the so-called\nmatrix product states, of an adiabatic quantum algorithm. Finally, in Chapter 6\nwe consider the behavior of some families of quantum algorithms from the\nperspective of majorization theory. The structure within each Chapter is such\nthat the last section always summarizes the basic results. Some general\nconclusions and possible future directions are briefly discussed in Chapter 7.\nAppendix A, Appendix B and Appendix C respectively deal with some basic notions\non majorization theory, conformal field theory, and classical complexity\ntheory.",
"arxiv_id": "quant-ph/0608013",
"authors": [
"Roman Orus"
],
"categories": [
"quant-ph",
"cond-mat.str-el",
"hep-th"
],
"title": "Entanglement, quantum phase transitions and quantum algorithms",
"url": "https://arxiv.org/abs/quant-ph/0608013"
},
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