dorsal/arxiv
View SchemaMacroscopic entanglement in Quantum Computation
| Authors | Akihisa Ukena, Akira Shimizu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505057 |
| URL | https://arxiv.org/abs/quant-ph/0505057 |
Abstract
We investigate macroscopic entanglement of quantum states in quantum computers, where we say a quantum state is entangled macroscopically if the state has superposition of macroscopically distinct states. The index $p$ of the macroscopic entanglement is calculated as a function of the step of the computation, for Grover's quantum search algorithm and Shor's factoring algorithm. It is found that whether macroscopically entangled states are used or not depends on the numbers and properties of the solutions to the problem to be solved. When the solutions are such that the problem becomes hard in the sense that classical algorithms take more than polynomial steps to find a solution, macroscopically entangled states are always used in Grover's algorithm and almost always used in Shor's algorithm. Since they are representative algorithms for unstructured and structured problems, respectively, our results support strongly the conjecture that quantum computers utilize macroscopically entangled states when they solve hard problems much faster than any classical algorithms.
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"abstract": "We investigate macroscopic entanglement of quantum states in quantum\ncomputers, where we say a quantum state is entangled macroscopically if the\nstate has superposition of macroscopically distinct states. The index $p$ of\nthe macroscopic entanglement is calculated as a function of the step of the\ncomputation, for Grover\u0027s quantum search algorithm and Shor\u0027s factoring\nalgorithm. It is found that whether macroscopically entangled states are used\nor not depends on the numbers and properties of the solutions to the problem to\nbe solved. When the solutions are such that the problem becomes hard in the\nsense that classical algorithms take more than polynomial steps to find a\nsolution, macroscopically entangled states are always used in Grover\u0027s\nalgorithm and almost always used in Shor\u0027s algorithm. Since they are\nrepresentative algorithms for unstructured and structured problems,\nrespectively, our results support strongly the conjecture that quantum\ncomputers utilize macroscopically entangled states when they solve hard\nproblems much faster than any classical algorithms.",
"arxiv_id": "quant-ph/0505057",
"authors": [
"Akihisa Ukena",
"Akira Shimizu"
],
"categories": [
"quant-ph"
],
"title": "Macroscopic entanglement in Quantum Computation",
"url": "https://arxiv.org/abs/quant-ph/0505057"
},
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"execution_id": "74037d40-cf3b-49e6-a1dd-0e81f6859316",
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