dorsal/arxiv
View SchemaA Quantitative Measure of Interference
| Authors | Daniel Braun, Bertrand Georgeot |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510159 |
| URL | https://arxiv.org/abs/quant-ph/0510159 |
| DOI | 10.1103/PhysRevA.73.022314 |
| Journal | Phys. Rev. A 73, 022314 (2006) |
Abstract
We introduce an interference measure which allows to quantify the amount of interference present in any physical process that maps an initial density matrix to a final density matrix. In particular, the interference measure enables one to monitor the amount of interference generated in each step of a quantum algorithm. We show that a Hadamard gate acting on a single qubit is a basic building block for interference generation and realizes one bit of interference, an ``i-bit''. We use the interference measure to quantify interference for various examples, including Grover's search algorithm and Shor's factorization algorithm. We distinguish between ``potentially available'' and ``actually used'' interference, and show that for both algorithms the potentially available interference is exponentially large. However, the amount of interference actually used in Grover's algorithm is only about 3 i-bits and asymptotically independent of the number of qubits, while Shor's algorithm indeed uses an exponential amount of interference.
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"abstract": "We introduce an interference measure which allows to quantify the amount of\ninterference present in any physical process that maps an initial density\nmatrix to a final density matrix. In particular, the interference measure\nenables one to monitor the amount of interference generated in each step of a\nquantum algorithm. We show that a Hadamard gate acting on a single qubit is a\nbasic building block for interference generation and realizes one bit of\ninterference, an ``i-bit\u0027\u0027. We use the interference measure to quantify\ninterference for various examples, including Grover\u0027s search algorithm and\nShor\u0027s factorization algorithm. We distinguish between ``potentially\navailable\u0027\u0027 and ``actually used\u0027\u0027 interference, and show that for both\nalgorithms the potentially available interference is exponentially large.\nHowever, the amount of interference actually used in Grover\u0027s algorithm is only\nabout 3 i-bits and asymptotically independent of the number of qubits, while\nShor\u0027s algorithm indeed uses an exponential amount of interference.",
"arxiv_id": "quant-ph/0510159",
"authors": [
"Daniel Braun",
"Bertrand Georgeot"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"nlin.CD"
],
"doi": "10.1103/PhysRevA.73.022314",
"journal_ref": "Phys. Rev. A 73, 022314 (2006)",
"title": "A Quantitative Measure of Interference",
"url": "https://arxiv.org/abs/quant-ph/0510159"
},
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