Physics Department, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA.
Department of Physics, University of Central Florida, 4111 Libra Drive, Orlando, Florida 32816, USA.
Nat Commun. 2017 May 12;8:15303. doi: 10.1038/ncomms15303.
Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.
经典计算到统计力学模型的映射在解决一些复杂的计算问题方面取得了显著的成功。然而，这些映射显示出热力学相变，这可能会阻止即使对于那些已知可以在多项式时间内解决的简单问题也无法得到解决方案。在这里，我们将通用可逆经典计算映射到一个平面顶点模型上，该模型不显示任何整体经典热力学相变，与计算电路无关。在我们的方法中，计算的解决方案被编码在顶点模型的基态中，其复杂性反映在系统松弛到基态的动力学中。我们使用带有和不带有“学习”的热退火来探索典型的计算问题。我们还将顶点模型映射到 D-Wave 机器的 Chimera 架构中，从而为基于量子退火的最新实现的可逆经典计算开辟了一种方法。
