Response of quantum spin networks to attacks
Response of quantum spin networks to attacks
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DOI：
10.1088/2632-072x/abf5c2
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Bhuvanesh Sundar;M. Walschaers;V. Parigi;L. Carr
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文献类型：
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作者：
Bhuvanesh Sundar;M. Walschaers;V. Parigi;L. Carr
我们研究了定义在我们印记的网络(例如，像Erdos-Renyi这样的非复杂随机网络，或者像Watts-Stogue atz和Barabasi-Albert这样的复杂网络)上定义的自旋模型的基态，以及它们对我们用网络攻击建模的解码过程的响应。我们通过计算一个紧急网络的网络度量分布来量化这些基态的复杂性及其对攻击的响应，该网络的链路权重是自旋之间的成对互信息。我们专注于投射测量旋转的攻击。我们发现，处于基态的涌现网络并不满足通常的复杂性标准，并且它们的平均性质被哈密顿量中的一个无量纲参数很好地捕捉到。虽然经典网络对攻击的响应已经得到了很好的研究，其中经典复杂网络比随机网络更具稳健性，但我们发现我们的量子网络的结果与直觉相反。我们发现，定义在不同类型的印迹网络上的哈密顿量的基态对我们的所有攻击的响应是相似的，并且这些攻击以一个恒定的因子改变了涌现网络的平均性质。平均场理论解释了相对密集网络的这些结果，但我们也发现了偏离平均场理论有效性的简单重标度行为。我们的计算表明，与经典情况相比，复杂的自旋网络并不比非复杂的自旋网络更能抵抗投射测量攻击，而且可能还有其他量子攻击。了解自旋网络对退相干和攻击的反应，将有助于理解开放量子系统的物理学，并有助于设计强大的复杂量子系统--从长远来看，甚至可能是一个强大的量子互联网--最大限度地抵抗退相干。
We investigate the ground states of spin models defined on networks that we imprint (e.g., non-complex random networks like Erdos–Renyi, or complex networks like Watts–Strogatz, and Barabasi–Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counter-intuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems—possibly even a robust quantum internet in the long run—that is maximally resistant to decoherence.