Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde

Towards a Calculus of Echo State Networks

Reservoir computing is a recent trend in neural networks which uses the dynamical perturbations on the phase space of a system to compute a desired target function. We present how one can formulate an expectation of system performance in a simple class of reservoir computing called echo state networks. In contrast with previous theoretical frameworks, which only reveal an upper bound on the total memory in the system, we analytically calculate the entire memory curve as a function of the structure of the system and the properties of the input and the target function. We demonstrate the precision of our framework by validating its result for a wide range of system sizes and spectral radii. Our analytical calculation agrees with numerical simulations. To the best of our knowledge this work presents the first exact analytical characterization of the memory curve in echo state networks