Latest updates on Quantum Approximate Optimization Algorithm part3(Quantum Computing)
- Connection between single-layer Quantum Approximate Optimization Algorithm interferometry and thermal distributions sampling(arXiv)
Author : Pablo Díez-Valle, Diego Porras, Juan José García-Ripoll
Abstract : The Quantum Approximate Optimization Algorithm (QAOA) is an algorithm originally proposed to find approximate solutions to Combinatorial Optimization problems on quantum computers. However, the algorithm has also attracted interest for sampling purposes since it was theoretically demonstrated under reasonable complexity assumptions that one layer of the algorithm already engineers a probability distribution beyond what can be simulated by classical computers. In this regard, a recent study has shown as well that, in universal Ising models, this global probability distribution resembles pure but thermal-like distributions at a temperature that depends on internal correlations of the spin model. In this work, through an interferometric interpretation of the algorithm, we extend the theoretical derivation of the amplitudes of the eigenstates, and the Boltzmann distributions generated by single-layer QAOA. We also review the implications that this behavior has from both a practical and fundamental perspective.
2.Local to Global: A Distributed Quantum Approximate Optimization Algorithm for Pseudo-Boolean Optimization Problems (arXiv)
Author : Bo Yue, Shibei Xue, Yu Pan, Min Jiang, Daoyi Dong
Abstract : With the rapid advancement of quantum computing, Quantum Approximate Optimization Algorithm (QAOA) is considered as a promising candidate to demonstrate quantum supremacy, which exponentially solves a class of Quadratic Unconstrained Binary Optimization (QUBO) problems. However, limited qubit availability and restricted coherence time challenge QAOA to solve large-scale pseudo-Boolean problems on currently available Near-term Intermediate Scale Quantum (NISQ) devices. In this paper, we propose a distributed QAOA which can solve a general pseudo-Boolean problem by converting it to a simplified Ising model. Different from existing distributed QAOAs’ assuming that local solutions are part of a global one, which is not often the case, we introduce community detection using Louvian algorithm to partition the graph where subgraphs are further compressed by community representation and merged into a higher level subgraph. Recursively and backwards, local solutions of lower level subgraphs are updated by heuristics from solutions of higher level subgraphs. Compared with existing methods, our algorithm incorporates global heuristics into local solutions such that our algorithm is proven to achieve a higher approximation ratio and outperforms across different graph configurations. Also, ablation studies validate the effectiveness of each component in our method.
