Time evolution of complexity in Abelian gauge theories
Time evolution of complexity in Abelian gauge theories
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DOI：
10.1103/physrevd.96.126001
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发表时间：
2017-07
影响因子：
5
通讯作者：
K. Hashimoto;Norihiro Iizuka;Sotaro Sugishita
中科院分区：
文献类型：
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作者：
K. Hashimoto;Norihiro Iizuka;Sotaro Sugishita
量子复杂性被推测为通过规范引力对应来探测黑洞视界（或虫洞）内部。为了更好地理解这种对应关系，我们研究了阿贝尔纯规范理论复杂性的时间演化。为此，我们将U(1)规范群离散为ZN，将连续时空离散为晶格时空，这使得我们能够为这些规范理论定义一个通用门集，并明确地评估复杂性的时间演化。我们发现，为了实现大的复杂性~ exp（熵），这是拥有对偶黑洞所必需的推测标准之一，阿贝尔规范理论需要最大限度地非局域。
Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U(1) gauge group as ZN and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ∼exp(entropy), which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.