Second law of quantum complexity
Second law of quantum complexity
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DOI：
10.1103/physrevd.97.086015
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发表时间：
2018-04-25
影响因子：
5
通讯作者：
Susskind, Leonard
中科院分区：
文献类型：
--
作者：
Brown, Adam R.;Susskind, Leonard
我们论证了量子复杂性热力学的存在，它包含了“复杂性第二定律”。“为了指导我们，我们推导出K个量子比特的量子系统的计算（电路）复杂性与具有2（K）个自由度的相关经典系统的位置熵之间的对应关系。我们还认为经典系统的动力学熵等价于量子哈密顿量的Kolmogorov复杂性。我们观察到，量子系统的复杂性增长的预期模式与经典系统的熵增长平行。我们认为，具有小于最大复杂性（不复杂性）的属性是一种资源，可以用来执行有向量子计算。虽然这篇论文主要不是关于黑洞的，但我们发现了一个令人惊讶的解释，即在黑洞视界后面的时空的可访问量。
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "second law of complexity." To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of K qubits, and the positional entropy of a related classical system with 2(K) degrees of freedom. We also argue that the kinetic entropy of the classical system is equivalent to the Kolmogorov complexity of the quantum Hamiltonian. We observe that the expected pattern of growth of the complexity of the quantum system parallels the growth of entropy of the classical system. We argue that the property of having less-than-maximal complexity (uncomplexity) is a resource that can be expended to perform directed quantum computation. Although this paper is not primarily about black holes, we find a surprising interpretation of the uncomplexity resource as the accessible volume of spacetime behind a black hole horizon.