arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0705.4077quant-ph
收藏

量子系统的力量在一条线上

The power of quantum systems on a line

Dorit Aharonov, Daniel Gottesman, Sandy Irani, Julia Kempe

摘要:

我们研究量子粒子(每个有限维)排列在一条线上的计算强度。首先,我们证明了使用一维量子系统(每个粒子有9个态)进行通用绝热量子计算是可能的。这可能对有兴趣建造绝热量子计算机的实验学家有实际意义。基于同样的结构,但有一些额外的技术努力和12个状态,每个粒子,我们表明,近似的基态能量的系统组成的一行量子粒子的问题是QMA-完全的,QMA是一个量子模拟NP。这与类似的经典问题(即具有最近邻约束的一维MAX-2-SAT)在P中的事实形成鲜明对比。QMA完备性结果的证明需要超出该领域常用技术的额外想法:并不是所有的非法配置都可以通过本地检查排除,所以我们排除了这些非法配置,因为它们在将来会,演变成一个在当地被视为非法的国家。我们的构造意味着(假设量子丘奇-图灵命题和量子计算机不能有效地解决QMA完全问题),存在一维系统,在任何温度下都需要指数时间弛豫到它们的基态,使它们成为一维自旋玻璃的候选者。

英文摘要:

We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Our construction implies (assuming the quantum Church-Turing thesis and that quantum computers cannot efficiently solve QMA-complete problems) that there are one-dimensional systems which take an exponential time to relax to their ground states at any temperature, making them candidates for being one-dimensional spin glasses.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑