Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the hardness of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.
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Quantum Social Computing Approaches for Influence Maximization
Influence Maximization (IM), which seeks a small set of important nodes that spread the influence widely into the network, is a fundamental problem in social networks. It finds applications in viral marketing, epidemic control, and assessing cascading failures within complex systems. Despite the huge amount of effort, finding near-optimal solutions for IM is difficult due to its NP-completeness. In this paper, we propose the first social quantum computing approaches for IM, aiming to retrieve near-optimal solutions. We propose a two-phase algorithm that 1) converts IM into a Max-Cover instance and 2) provides efficient quadratic unconstrained binary optimization formulations to solve the Max-Cover instance on quantum annealers. Our experiments on the state-of-the-art D-Wave annealer indicate better solution quality compared to classical simulated annealing, suggesting the potential of applying quantum annealing to find high-quality solutions for IM.
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- Award ID(s):
- 2229075
- NSF-PAR ID:
- 10477831
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- GLOBECOM 2022 - 2022 IEEE Global Communications Conference
- Page Range / eLocation ID:
- 5832 to 5837
- Subject(s) / Keyword(s):
- ["Quantum social computing","influence maximization","quantum annealing"]
- Format(s):
- Medium: X
- Location:
- Rio de Janeiro, Brazil
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/GLOBECOM48099.2022.10000698
