Detecting Multiple Communities Using Quantum Annealing on the D-Wave System

A very important problem in combinatorial optimization is partitioning a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences. The problem of community detection is a twofold problem that consists of determining the number of communities and, at the same time, finding those communities. This drastically increases the solution space for heuristics to work on, compared to traditional graph partitioning problems. In many of the scientific domains in which graphs are used, there is the need to have the ability to partition a graph into communities with the ``highest quality'' possible since the presence of even small isolated communities can become crucial to explain a particular phenomenon. We have explored community detection using the power of quantum annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out that the problem of detecting at most two communities naturally fits into the architecture of a quantum annealer with almost no need of reformulation. This paper addresses a systematic study of detecting two or more communities in a network using a quantum annealer

Network Community Detection On Small Quantum Computers

In recent years a number of quantum computing devices with small numbers of qubits became available. We present a hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size. 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. We demonstrate it to solve the 2-community detection problem on graphs of size up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. Our results demonstrate that QLS perform 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

Spatial Dynamics of Pandemic Influenza in a Massive Artificial Society

EpiSimS is a massive simulation of the movements, activities, and social interactions of individuals in realistic synthetic populations, and of the dynamics of contagious disease spread on the resulting social contact network. This paper describes the assumptions and methodology in the EpiSimS model. It also describes and presents a simulation of the spatial dynamics of pandemic influenza in an artificial society constructed to match the demographics of southern California. As an example of the utility of the massive simulation approach, we demonstrate a strong correlation between local demographic characteristics and pandemic severity, which gives rise to previously unanticipated spatial pandemic hotspots. In particular, the average household size in a census tract is strongly correlated with the clinical attack rate computed by the simulation. Public heath agencies with responsibility for communities having relatively high population per household should expect to be more severely hit by a pandemic.Agent Based Modeling, Computer Simulation, Epidemic Simulation, Public Health Policy

Quantum Local Search for Graph Community Detection

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

Quantum Isomer Search

Isomer search or molecule enumeration refers to the problem of finding all the isomers for a given molecule. Many classical search methods have been developed in order to tackle this problem. However, the availability of quantum computing architectures has given us the opportunity to address this problem with new (quantum) techniques. This paper describes a quantum isomer search procedure for determining all the structural isomers of alkanes. We first formulate the structural isomer search problem as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO formulation is for general use on either annealing or gate-based quantum computers. We use the D-Wave quantum annealer to enumerate all structural isomers of all alkanes with fewer carbon atoms (n < 10) than Decane (C10H22). The number of isomer solutions increases with the number of carbon atoms. We find that the sampling time needed to identify all solutions scales linearly with the number of carbon atoms in the alkane. We probe the problem further by employing reverse annealing as well as a perturbed QUBO Hamiltonian and find that the combination of these two methods significantly reduces the number of samples required to find all isomers.Comment: 20 pages, 9 figure

Protein annotation as term categorization in the gene ontology using word proximity networks

We addressed BioCreAtIvE Task 2, the problem of annotation of a protein with a node in the Gene Ontology (GO). We approached the task as a problem of categorizing terms derived from the document neighborhood of the given protein in the given document into nodes in the GO based on the lexical overlaps with terms on GO nodes and terms identified as related to those nodes. The system incorporates NLP components such as a morphological normalizer, a named entity recognizer, a statistical term frequency analyzer, and an unsupervised method for expanding words associated with GO ids based on a probability measure that captures word proximity (Rocha, 2002). The categorization methodology uses our novel Gene Ontology Categorizer (GOC) methodology (Joslyn et al. 2004) to select GO nodes as cluster heads for the terms in the input set based on the structure of the GO. Pre-processing Swiss-Prot and TrEMBL IDs were provided as input identifiers for the protein, so we needed to establish a set of names by which that protein could be referenced in the text. We made use of both the gene name and protein names that are in Swiss-Prot itself, when available, and a collection of synonyms constructed by Procter &amp; Gamble Company. The fallback case was to us

Multilevel Combinatorial Optimization Across Quantum Architectures

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the Post Moore\u27s 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\u27s quantum annealer and IBM\u27s 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