Quadratic Unconstrained Binary Optimization (QUBO) modeling has become a unifying framework for solving a wide variety of both unconstrained as well as constrained optimization problems. More recently, QUBO (or equivalent $-1∕+1$ Ising Spin) models are a requirement for quantum annealing computers. Noisy Intermediate-Scale Quantum (NISQ) computing refers to classical computing preparing or compiling problem instances for compatibility with quantum hardware architectures. The process of converting a constrained problem to a QUBO compatible quantum annealing problem is an important part of the quantum compiler architecture and specifically when converting constrained models to unconstrained the choice of penalty magnitude is not trivial because using a large penalty to enforce constraints can overwhelm the solution landscape, while having too small a penalty allows infeasible optimal solutions. In this paper we present NISQ approaches to bound the magnitude of the penalty scalar $M$ and demonstrate efficacy on a benchmark set of problems having a single equality constraint and present a QUBO partitioning approach validated by experimentation.

二次无约束二进制优化（QUBO）建模已成为一个统一的框架，用于解决各种无约束和有约束的优化问题。最近，QUBO（或同等水平$-\mathrm{1个}∕+\mathrm{1个}$Ising Spin）模型是量子退火计算机的要求。噪声中级量子（NISQ）计算是指经典计算准备或编译问题实例以与量子硬件体系结构兼容。将约束问题转换为与QUBO兼容的量子退火问题的过程是量子编译器体系结构的重要组成部分，特别是在将约束模型转换为无约束条件时，惩罚量的选择并不是一件容易的事，因为使用大的惩罚来强制约束会不堪重负。解决方案格局，尽管代价太小，却无法实现最佳解决方案。在本文中，我们提出了NISQ方法来约束惩罚标量的大小$\mathrm{中号}$ 并展示了对具有单一等式约束的基准问题集的有效性，并提出了通过实验验证的QUBO分区方法。