On the quantum adiabatic evolution with the most general system Hamiltonian
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In this paper, we study the problem that when quantum adiabatic evolution with the most general form of system Hamiltonian will get failed. Here the most general form means that the initial and final Hamiltonians are just designed according to the adiabatic theorem in quantum mechanics. As we will see, even in this most general model of quantum adiabatic evolution, it still exists the possibility that the quantum adiabatic computation can fail totally if some condition is satisfied, which implies the time complexity of the quantum algorithm is infinity. That is, here we propose a rather general criterion for judging whether a quantum adiabatic evolution is successful. This result largely extends the authors’ previous research on this topic, and it may be seen as a further important clue for us when designing quantum algorithms in the framework of adiabatic evolution for some practical problems.
KeywordsGeneral system Hamiltonian Quantum adiabatic evolution Quantum computation
Jie Sun gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2017M620322, the support from the National Natural Science Foundation of China under Grant No. 61402188, the fund by Priority for the Postdoctoral Scientific and Technological Program of Hubei Province in 2017, and the Seed Foundation of Huazhong University of Science and Technology under Grant No. 2017KFYXJJ070. This work is also supported by the Science and Technology Program of Shenzhen of China under Grant Nos. JCYJ 20170818160208570 and JCYJ 20180306124612893. Finally, the authors should appreciate greatly the anonymous reviewer for helpful comments and advice on the revision of the paper which make it be in its present form.
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