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A New Approach to the Quantum Adiabatic Condition |
| GUO Chu1**, DUAN Qian-Heng1, CHEN Ping-Xing1,2 |
1Department of Physics, National University of Defense Technology, Changsha 410073
2State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073
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| Cite this article: |
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GUO Chu, DUAN Qian-Heng, CHEN Ping-Xing 2012 Chin. Phys. Lett. 29 100301 |
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Abstract The quantum adiabatic theorem is the basis of adiabatic quantum computation. However, the exact necessary and sufficient conditions for adiabatic evolution are still under debate. We discuss the adiabatic condition of a system undergoing a special evolution route, and obtain an explicit formula that is necessary and sufficient for the adiabatic evolution in this route. Based on this formula, we find that the traditional adiabatic condition is neither sufficient nor necessary. Finally, we show that no adiabatic process can occur even the evolution speed goes to 0 in some examples, which is surprising since the adiabatic theorem states that if the evolution of a system is slow enough, the adiabatic process could occur.
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Received: 26 June 2012
Published: 01 October 2012
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| PACS: |
03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.65.Ca
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(Formalism)
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03.67.Lx
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(Quantum computation architectures and implementations)
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