Quantum Enhanced Inference in Markov Logic Networks

Abstract

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

Machine learning & artificial intelligence in the quantum domain: a review of recent progress

“…This possibility is also sure to inspire novel QML ideas. Moving on from BMs, in recent work (Wittek and Gogolin, 2017), the authors have also shown how suitable annealing architectures may be useful to speed-up the performing of probabilistic inference in so-called Markov logic networks 108 . This task involves the estimation of partition functions of arising from statistical models, concretely Markov random fields, which include the Ising model as a special case.…”

Scaling reconfigurable emulation of quantum algorithms at high precision and high throughput

“…This implementation has double the resource requirements of the first architecture but has the benefit of improvement in execution time. The time complexity is determined as in (20) and the space complexity is given by (21).…”

“…An experimental realization of a quantum computing silicon chip was fabricated in the work of Qiang et al 18 In contrast to other realizations, this quantum chip does not use product of unitary operation architecture as proposed in the work of Benioff, 1 it employed the linear combinations of unitary (LCU) operations architecture, proposed in the work of Gui-Lu. 19 The LCU has found extensive applications in quantum algorithms recently, as reviewed in the work of Shao et al, 20 extending to quantum machine learning, 21 secure multiparty computing, 22 and passive error correction. 23 Despite having operational quantum hardware, there are critical problems and challenges 24 in these systems that need to be solved.…”

Quantum Informatics: Overview of the Main Achievements

“…В [60] рассмотрены марковские логические сети (MLNs), объединяющие две противоположные школы в машинном обучении и искусственном интеллекте: причинно-следственные сети, которые очень хорошо учитывают неопределенность, и логику первого порядка, которая допускает формальные выводы. MLN -это, по сути, логический шаблон первого порядка для создания сетей Маркова.…”

“…MLN имеет множество регулярных симметричных структур, которые разумно использовать и на уровне первого порядка, и в генерируемой сети Маркова. Различными способами проанализированы созданные графовые структуры и определено, в какой степени квантовые протоколы могут использоваться для ускорения выборки Гиббса с помощью схем подготовки и измерения состояния [60]. На основе анализа различных подходов, оценки их преимуществ, теоретических ограничений, возможностей реализации сделан также вывод, что прямое применение полученного результата приводит к экспоненциальному ускорению по сравнению с классическими эвристиками, что подтверждает их потенциальную полезность для применения в машинном обучении.…”