论文标题
在经典和量子计算机上进行混合二进制优化的多块ADMM启发式方法
Multi-block ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers
论文作者
论文摘要
目前正在提倡（并局限于）通过量子启发式方法对当前嘈杂的量子设备上的解决组合优化问题，并通过量子启发式方法进行平等约束。这是使用例如变异量子本质量（VQE）和量子近似优化算法（QAOA）来实现的。我们提出了一种基于分解的方法，以扩展当前方法对“二次加凸”混合二进制优化（MBO）问题的适用性，以解决一类广泛的现实世界优化问题。在MBO框架中，我们表明乘数的交替方向方法（ADMM）可以将MBO分为二进制不受约束的问题（可以用量子算法解决），并连续约束凸出的凸子问题（可以用经典优化溶液便宜地求解）。然后，通过使用VQE和QAOA在Qiskit实施的量子电路（一个开源量子计算软件开发框架上实现的量子电路上）在几个优化问题上获得的数值结果来展示该方法的有效性。
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, e.g., the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework, we show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms), and continuous constrained convex subproblems (that can be solved cheaply with classical optimization solvers). The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit, an open-source quantum computing software development framework.
