dorsal/arxiv
View SchemaQuantum Computation, Complexity, and Many-Body Physics
| Authors | Rolando D. Somma |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512209 |
| URL | https://arxiv.org/abs/quant-ph/0512209 |
Abstract
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.
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"abstract": "Recently developed quantum algorithms suggest that quantum computers can\nsolve certain problems and perform certain tasks more efficiently than\nconventional computers. Among other reasons, this is due to the possibility of\ncreating non-classical correlations, or quantum entanglement, which is a\nphenomena hard or impossible to reproduce by classical-information methods.\n In this thesis I first investigate the simulation of quantum systems on a\nquantum computer constructed of two-level quantum elements or qubits. For this\npurpose, I present algebra mappings that allow one to obtain physical\nproperties and compute correlation functions of fermionic, anyonic, and bosonic\nsystems with such a computer. The results obtained show that the complexity of\npreparing a quantum state which contains the desired information for the\ncomputation is crucial.\n Second, I present a wide class of quantum computations, which could involve\nentangled states, that can be simulated with the same efficiency on both types\nof computers. The notion of generalized quantum entanglement then naturally\nemerges. This generalization of entanglement is based on the idea that\nentanglement is an observer-dependent concept, that is, relative to a set of\npreferred observables.",
"arxiv_id": "quant-ph/0512209",
"authors": [
"Rolando D. Somma"
],
"categories": [
"quant-ph",
"cond-mat.other"
],
"title": "Quantum Computation, Complexity, and Many-Body Physics",
"url": "https://arxiv.org/abs/quant-ph/0512209"
},
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