Related papers: Deep Conditional Measure Quantization
By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary…
Quantization is a technique for creating efficient Deep Neural Networks (DNNs), which involves performing computations and storing tensors at lower bit-widths than f32 floating point precision. Quantization reduces model size and inference…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
Quantization is a widely used technique to compress and accelerate deep neural networks. However, conventional quantization methods use the same bit-width for all (or most of) the layers, which often suffer significant accuracy degradation…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
Quantum correlations in a physical system are usually studied with respect to a unique (fixed) decomposition of the system into subsystems, without fully exploiting the rich structure of the state-space. Here, we show several examples in…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Upon compressing perceptually relevant signals, conventional quantization generally results in unnatural outcomes at low rates. We propose distribution preserving quantization (DPQ) to solve this problem. DPQ is a new quantization concept…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
Quantification, also known as class prevalence estimation, is the supervised learning task in which a model is trained to predict the prevalence of each class in a given bag of examples. This paper investigates the application of deep…
With the development of deep neural networks, the size of network models becomes larger and larger. Model compression has become an urgent need for deploying these network models to mobile or embedded devices. Model quantization is a…
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…
We propose a probabilistic framework for dynamic quantization of neural networks that allows for a computationally efficient input-adaptive rescaling of the quantization parameters. Our framework applies a probabilistic model to the…
To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…