We describe Kitaev's result from 1999, in which he defines the complexity class QMA, the quantum analog of the class NP, and shows that a natural extension of 3-SAT, namely local Hamiltonians, is QMA complete. The result builds upon the classical Cook-Levin proof of the NP completeness of SAT, but differs from it in several fundamental ways, which we highlight. This result raises a rich array of open problems related to quantum complexity, algorithms and entanglement, which we state at the end of this survey. This survey is the extension of lecture notes taken by Naveh for Aharonov's quantum computation course, held in Tel Aviv University, 2001.
翻译：我们描述Kitaev1999年的结果,他在其中界定了QMA的复杂等级,即NP类的量子类比,并表明3SAT的自然延伸,即当地的汉密尔顿人,是QMA的完成,其结果以古典的Cook-Levin证据为基础,证明了SAT的NP完整性,但与我们强调的一些基本方式不同。这一结果产生了大量与量子复杂性、算法和纠结有关的公开问题,我们在这次调查结束时指出这些问题。这项调查是纳韦为2001年特拉维夫大学的Aharonov量子计算课程所作的演讲说明的延伸,该说明是2001年在特拉维夫大学举行的Aharonov的量子计算课程。
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