Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks

Quantum systems interacting with an unknown environment are notoriously difficult to model, especially in presence of non-Markovian and non-perturbative effects. Here we introduce a neural network based approach, which has the mathematical simplicity of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, but is able to model non-Markovian effects in different regimes. This is achieved by using recurrent neural networks for defining Lindblad operators that can keep track of memory effects. Building upon this framework, we also introduce a neural network architecture that is able to reproduce the entire quantum evolution, given an initial state. As an application we study how to train these models for quantum process tomography, showing that recurrent neural networks are accurate over different times and regimes.Comment: 10 pages, 8 figure

Strategic adoption of logistics and supply chain management

© 2018, Emerald Publishing Limited. Purpose: The purpose of this paper is to develop a thorough understanding of the adoption of logistics and supply chain management (SCM) in practice, particularly at a strategic level, through an investigation of the four perspectives taxonomy of the relationship between logistics and SCM. Design/methodology/approach: Based on a comprehensive literature review, three specific research questions are proposed. The empirical work addresses these questions and comprised three phases: focussed interviews, a questionnaire survey and focus groups. Findings: The findings provide a usage profile of the four perspectives and indicate a divergence between the understanding and adoption of logistics and SCM principles and concepts at a strategic level in firms. The findings also identify the critical success factors (CSFs) and inhibitors to success in addressing this divergence. Research limitations/implications: The insights generated using the authors’ methodologically pluralist research design could be built upon to include case studies, grounded theory and action research. Replicating the research in other geographical areas could facilitate international comparisons. Practical implications: The findings allow practitioners to compare their perspectives on the relationship between logistics and SCM with those of their peers. The CSFs and inhibitors to success provide a rational basis for realising the strategic potential of logistics and SCM in practice. Originality/value: New insights are generated into practitioner perspectives vis-à-vis logistics vs SCM. A fresh understanding of those factors which drive and hinder the adoption of strategic SCM is also developed and presented

Learning hard quantum distributions with variational autoencoders

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. Our simulations show that deep networks give a better representation for states that are hard to sample from, while providing no benefit for random states. This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in first generation quantum hardware.Comment: v2: 9 pages, 3 figures, journal version with major edits with respect to v1 (rewriting of section "hard and easy quantum states", extended discussion on comparison with tensor networks