dorsal/arxiv
View SchemaMixing and Decoherence in Continuous-Time Quantum Walks on Cycles
| Authors | Leonid Fedichkin, Dmitry Solenov, Christino Tamon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509163 |
| URL | https://arxiv.org/abs/quant-ph/0509163 |
| Journal | Quantum Information and Computation, Vol. 6, No. 3 (2006), 263-276. |
Abstract
We prove analytical results showing that decoherence can be useful for mixing time in a continuous-time quantum walk on finite cycles. This complements the numerical observations by Kendon and Tregenna (Physical Review A 67 (2003), 042315) of a similar phenomenon for discrete-time quantum walks. Our analytical treatment of continuous-time quantum walks includes a continuous monitoring of all vertices that induces the decoherence process. We identify the dynamics of the probability distribution and observe how mixing times undergo the transition from quantum to classical behavior as our decoherence parameter grows from zero to infinity. Our results show that, for small rates of decoherence, the mixing time improves linearly with decoherence, whereas for large rates of decoherence, the mixing time deteriorates linearly towards the classical limit. In the middle region of decoherence rates, our numerical data confirms the existence of a unique optimal rate for which the mixing time is minimized.
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"abstract": "We prove analytical results showing that decoherence can be useful for mixing\ntime in a continuous-time quantum walk on finite cycles. This complements the\nnumerical observations by Kendon and Tregenna (Physical Review A 67 (2003),\n042315) of a similar phenomenon for discrete-time quantum walks. Our analytical\ntreatment of continuous-time quantum walks includes a continuous monitoring of\nall vertices that induces the decoherence process. We identify the dynamics of\nthe probability distribution and observe how mixing times undergo the\ntransition from quantum to classical behavior as our decoherence parameter\ngrows from zero to infinity. Our results show that, for small rates of\ndecoherence, the mixing time improves linearly with decoherence, whereas for\nlarge rates of decoherence, the mixing time deteriorates linearly towards the\nclassical limit. In the middle region of decoherence rates, our numerical data\nconfirms the existence of a unique optimal rate for which the mixing time is\nminimized.",
"arxiv_id": "quant-ph/0509163",
"authors": [
"Leonid Fedichkin",
"Dmitry Solenov",
"Christino Tamon"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information and Computation, Vol. 6, No. 3 (2006),\n 263-276.",
"title": "Mixing and Decoherence in Continuous-Time Quantum Walks on Cycles",
"url": "https://arxiv.org/abs/quant-ph/0509163"
},
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