dorsal/arxiv
View SchemaQuantum loop programs
| Authors | Mingsheng Ying, Yuan Feng |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605218 |
| URL | https://arxiv.org/abs/quant-ph/0605218 |
| Journal | Acta Informatica 47(4): 221-250 (2010) |
Abstract
Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops and describe its computational process. The notions of termination and almost termination are proposed for quantum loops, and the function computed by a quantum loop is defined. To show their expressive power, quantum loops are applied in describing quantum walks. Necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented. A quantum loop is said to be (almost) terminating if it (almost) terminates on any input state. We show that a quantum loop is almost terminating if and only if it is uniformly almost terminating. It is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop (almost) terminating. Moreover, a representation of the function computed by a quantum loop is given in terms of finite summations of matrices. To illustrate the notions and results obtained in this paper, two simplest classes of quantum loop programs, one qubit quantum loops, and two qubit quantum loops defined by controlled gates, are carefully examined.
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"abstract": "Loop is a powerful program construct in classical computation, but its power\nis still not exploited fully in quantum computation. The exploitation of such\npower definitely requires a deep understanding of the mechanism of quantum loop\nprograms. In this paper, we introduce a general scheme of quantum loops and\ndescribe its computational process. The notions of termination and almost\ntermination are proposed for quantum loops, and the function computed by a\nquantum loop is defined. To show their expressive power, quantum loops are\napplied in describing quantum walks. Necessary and sufficient conditions for\ntermination and almost termination of a general quantum loop on any mixed input\nstate are presented. A quantum loop is said to be (almost) terminating if it\n(almost) terminates on any input state. We show that a quantum loop is almost\nterminating if and only if it is uniformly almost terminating. It is observed\nthat a small disturbance either on the unitary transformation in the loop body\nor on the measurement in the loop guard can make any quantum loop (almost)\nterminating. Moreover, a representation of the function computed by a quantum\nloop is given in terms of finite summations of matrices. To illustrate the\nnotions and results obtained in this paper, two simplest classes of quantum\nloop programs, one qubit quantum loops, and two qubit quantum loops defined by\ncontrolled gates, are carefully examined.",
"arxiv_id": "quant-ph/0605218",
"authors": [
"Mingsheng Ying",
"Yuan Feng"
],
"categories": [
"quant-ph"
],
"journal_ref": "Acta Informatica 47(4): 221-250 (2010)",
"title": "Quantum loop programs",
"url": "https://arxiv.org/abs/quant-ph/0605218"
},
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