最优化问题奇偶公式化中的最小约束
Minimal Constraints in the Parity Formulation of Optimization Problems
摘要：
作为使用量子计算机解决优化问题的一种手段，该问题通常被重铸为伊辛自旋模型，其基态是优化问题的解。伊辛公式的另一个替代是Lechner-Hauke-Zoller模型，它具有最近邻四体约束的格点规范模型的形式。在这里，我们介绍了一种方法来找到所需的约束，以保持正确的基态的最小强度。在此基础上，我们推导出最小约束强度的上界和下界。我们发现，取决于问题类，指数范围从线性$α\propto 1$到二次$α\propto 2$缩放与逻辑量子比特的数量。
英文摘要：
As a means to solve optimization problems using quantum computers, the problem is typically recast into a Ising spin model whose ground-state is the solution of the optimization problem. An alternative to the Ising formulation is the Lechner-Hauke-Zoller model, which has the form of a lattice gauge model with nearest neighbor 4-body constraints. Here we introduce a method to find the minimal strength of the constraints which are required to conserve the correct ground-state. Based on this, we derive upper and lower bounds for the minimal constraints strengths. We find that depending on the problem class, the exponent ranges from linear $α\propto 1$ to quadratic $α\propto 2$ scaling with the number of logical qubits.
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