dorsal/arxiv
View SchemaUniversal construction for the unsorted quantum search algorithms
| Authors | Xijia Miao |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101126 |
| URL | https://arxiv.org/abs/quant-ph/0101126 |
Abstract
The multiple-quantum operator algebra formalism has been exploited to construct generally an unsorted quantum search algorithm. The exponential propagator and its corresponding effective Hamiltonian are constructed explicitly that describe in quantum mechanics the time evolution of a multi- particle two-state quantum system from the initial state to the output of the unsorted quantum search problem. The exponential propagator usually may not be compatible with the mathematical structure and principle of the search problem and hence is not a real quantum search network, but it can be further decomposed into a product of a series of the oracle unitary operations such as the selective phase-shift operations and the nonselective unitary operations which can be expressed further as a sequence of elementary building blocks such as one-qubit quantum gates and the two-qubit diagonal phase gates, resulting in that the decomposed propagator is compatible with the mathematical structure and principle of the search problem and thus, becomes a real quantum search network. The decomposition for the propagator can be achieved with the help of the operator algebra structure and symmetry of the effective Hamiltonian, and the properties of the multiple-quantum operator algebra spaces, especially the characteristic transformation behavior of the multiple-quantum operators under the z-axis rotations. It has been shown that the computational complexity of the search algorithm is dependent upon that of the numerical multidimensional integration and hence it is believed that the search algorithm could solve efficiently the unsorted search problem. An NMR device is also proposed to solve efficiently the unsorted search problem in polynomial time.
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"abstract": "The multiple-quantum operator algebra formalism has been exploited to\nconstruct generally an unsorted quantum search algorithm. The exponential\npropagator and its corresponding effective Hamiltonian are constructed\nexplicitly that describe in quantum mechanics the time evolution of a multi-\nparticle two-state quantum system from the initial state to the output of the\nunsorted quantum search problem. The exponential propagator usually may not be\ncompatible with the mathematical structure and principle of the search problem\nand hence is not a real quantum search network, but it can be further\ndecomposed into a product of a series of the oracle unitary operations such as\nthe selective phase-shift operations and the nonselective unitary operations\nwhich can be expressed further as a sequence of elementary building blocks such\nas one-qubit quantum gates and the two-qubit diagonal phase gates, resulting in\nthat the decomposed propagator is compatible with the mathematical structure\nand principle of the search problem and thus, becomes a real quantum search\nnetwork. The decomposition for the propagator can be achieved with the help of\nthe operator algebra structure and symmetry of the effective Hamiltonian, and\nthe properties of the multiple-quantum operator algebra spaces, especially the\ncharacteristic transformation behavior of the multiple-quantum operators under\nthe z-axis rotations. It has been shown that the computational complexity of\nthe search algorithm is dependent upon that of the numerical multidimensional\nintegration and hence it is believed that the search algorithm could solve\nefficiently the unsorted search problem. An NMR device is also proposed to\nsolve efficiently the unsorted search problem in polynomial time.",
"arxiv_id": "quant-ph/0101126",
"authors": [
"Xijia Miao"
],
"categories": [
"quant-ph"
],
"title": "Universal construction for the unsorted quantum search algorithms",
"url": "https://arxiv.org/abs/quant-ph/0101126"
},
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