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Bulletin of the American Physical Society

Quantum Local Search for Graph Community Detection

Ruslan Shaydulin, Hayato Ushijima‐Mwesigwa, Ilya Safro, Susan M. Mniszewski, Yuri Alexeev

Published Mar 4, 2019• 0 citations
OpenAlex

Abstract

We present Quantum Local Search (QLS) approach and demonstrate its efficacy by applying it to the problem of community detection in real-world networks. QLS is a hybrid algorithm that combines a classical machine with a small quantum device. QLS starts with an initial solution and searches its neighborhood, iteratively trying to find a better candidate solution. One of the main challenges of the quantum computing in NISQ era is the small number of available qubits. QLS addresses this challenge by using the quantum device only for the neighborhood search, which can be restricted to be small enough to fit on near-term quantum device. We implement QLS for modularity maximization graph clustering using QAOA on IBM Q Experience as a quantum local solver. We demonstrate the potential for quantum acceleration by showing that existing state-of-the-art optimization solvers cannot find a good solution to the local problems quickly and provide an estimate of how larger quantum devices can improve the performance of QLS.

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We present Quantum Local Search (QLS) approach and demonstrate its efficacy by applying it to the problem of community detection in real-world networks. QLS is a hybrid algorithm that combines a classical machine with a small quantum device. QLS starts with an initial solution and searches its neighborhood, iteratively trying to find a better candidate solution. One of the main challenges of the quantum computing in NISQ era is the small number of available qubits. QLS addresses this challenge by using the quantum device only for the neighborhood search, which can be restricted to be small enough to fit on near-term quantum device. We implement QLS for modularity maximization graph clustering using QAOA on IBM Q Experience as a quantum local solver. We demonstrate the potential for quantum acceleration by showing that existing state-of-the-art optimization solvers cannot find a good solution to the local problems quickly and provide an estimate of how larger quantum devices can improve the performance of QLS.
Abstract In recent years, a number of quantum computing devices with small numbers of qubits have become available. A hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size is presented. The proposed approach is applied to the network community detection problem. QLS is hardware‐agnostic and easily extendable to new quantum computing devices as they become available. It is demonstrated to solve the 2‐community detection problem on graphs of sizes of up to 410 vertices using the 16‐qubit IBM quantum computer and D‐Wave 2000Q, and compare their performance with the optimal solutions. The results herein demonstrate that QLS performs similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state‐of‐the‐art solvers in terms of quality of the solution including reaching the optimal solutions.
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore’s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this article, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. To demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave’s quantum annealer and IBM’s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitude larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution. Reproducibility : Our code and data are available at Reference [1].
ABSTRACT An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate neighbors. The size of this set is limited due to the computational costs required to run the method on classical processing units. We present a qubit‐efficient variational quantum algorithm that implements a quantum version of local search with only qubits and, therefore, can potentially work with classically intractable neighborhood sizes. Increasing the amount of quantum resources employed in the algorithm allows for a larger neighborhood size, improving the quality of obtained solutions. This trade‐off is crucial for present and near‐term quantum devices characterized by a limited number of logical qubits. Numerically simulating our algorithm, we successfully solved the largest graph coloring instance that was tackled by a quantum method. This achievement highlights the algorithm's potential for solving large‐scale combinatorial optimization problems on near‐term quantum devices.
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the Post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size and observe results comparable to state-of-the-art solvers.
We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. This hybrid algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We study the performance of this algorithm on 3-regular, Community, and Erdős-Rényi graphs with up to 100 nodes.
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.