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arXiv quant-ph/0303186quant-ph
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3-定域哈密顿量的冷却和低能态制备是完全的

Cooling and Low Energy State Preparation for 3-local Hamiltonians are FQMA-complete

Dominik Janzing, Pawel Wocjan, Thomas Beth

摘要:

我们引入了量子复杂性类ARMA。这门课描述了生成一个量子态的复杂性,这个量子态可以作为给定QMA问题的证明。从某种意义上说,FNP(与NP相关的函数问题)的量子类比。后者描述了为NP决策问题找到简洁证明的复杂性。而所有的FNP问题可以减少到NP,有没有明显的减少QMA,因为QMA的解决方案是一个量子态和QMA的解决方案的答案是或否。我们认为量子态生成器,得到经典的描述3-本地哈密顿量的n量子位作为输入,并准备这些系统的低能量状态作为输出。我们表明,这种状态发生器可以用来准备证人QMA问题。因此,低能态制备是完全的。我们的证明是Kitaev等人和Kempe与Regev关于k-局部Hamilton问题的QMA-完备性证明的推广。我们表明,可以解决的准备热平衡态的适当的温度下降作为一个多项式的倒数n。

英文摘要:

We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems associated with NP). The latter describes the complexity of finding a succinct proof for a NP decision problem. Whereas all FNP problems can be reduced to NP, there is no obvious reduction of FQMA to QMA since the solution of FQMA is a quantum state and the solution of QMA the answer yes or no. We consider quantum state generators that get classical descriptions of 3-local Hamiltonians on n qubits as input and prepare low energy states for these systems as output. We show that such state generators can be used to prepare witnesses for QMA problems. Hence low energy state preparation is FQMA-complete. Our proofs are extensions of the proofs by Kitaev et al. and Kempe and Regev for the QMA-completeness of k-local Hamiltonian problems. We show that FQMA can be solved by preparing thermal equilibrium states with an appropriate temperature decreasing as the reciprocal of a polynomial in n.

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