使经典基态自旋计算具有容错性
Making Classical Ground State Spin Computing Fault-Tolerant
摘要：
我们研究一个经典的确定性计算模型，其中经典系统的基态是计算的空间历史。该模型与量子点元胞自动机以及最近的通用绝热量子计算结构有关。在其最原始的形式中，在该模型中构造的系统在非零温度下工作时不能以无误差的方式进行计算。然而，通过利用该模型的配分函数和概率经典电路之间的映射，我们能够表明，它是可能的，使该模型有效地无误差。我们通过使用容错经典计算中的技术来实现这一点，并且结果是，如果温度低于临界温度，则系统可以有效地无错误地计算。我们进一步将这个模型与计算复杂性联系起来，并证明了关于有限温度经典自旋系统的某个问题对于复杂性类Merlin-Arthur是完全的。这在某些多体自旋系统的物理行为和计算复杂性之间提供了一个有趣的联系。
英文摘要：
We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.
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