This paper proposes a hybrid model of machine learning, based at the principles of quantum mechanics in conjunction to Bayes theorem. With such construction, it is tested onto a scenario dictated by the Mitchell criteria. By assuming stochastic system whose main dependence is through time, the proposed model exhibits a high experience probability just at the beginning of processes. The results of this paper would corroborate the hypothesis that stochastic system might be strongly dependent at the very beginning or initial conditions.
This paper proposes a hybrid model of machine learning, based at the principles of quantum mechanics in conjunction to Bayes theorem. With such construction, it is tested onto a scenario dictated by the Mitchell criteria. By assuming stochastic system whose main dependence is through time, the proposed model exhibits a high experience probability just at the beginning of processes. The results of this paper would corroborate the hypothesis that stochastic system might be strongly dependent at the very beginning or initial conditions.
A theory consisting in quantum mechanics and theorem of Bayes, is presented. In essence, the Bayes probability has been built from two subspaces. While in one some quantum measurements are done, in the another it is seen that the probabilities acquire their highest values. Thus, the validity of a prior probability makes sense is there is a clear difference between the done measurement of probability amplitude. Thus, the principles of machine learning compacted in the criteria of Tom Mitchell have been employed. The simulations have shown that the size of space has direct impact on the prior probability that presumably would get low values of probability in a limited subspace. These values have turned out to be strongly correlated to the times in which measurements are done in a big space. Therefore, it is evident the prospective applicability of this novel approach in all those scenarios that require of a quantum measurement in separated times.
We present a theory of Machine Learning based entirely on the formalism of Quantum Mechanics from the fact that the diverse instances on the application of the algorithms would contain certain concepts linked to stochastic. In this manner, the probabilistic formalism of the Quantum Mechanics might be well applied. Thus, we implement the Mitchell's criteria with mathematical methodologies based on the Hilbert's space as well as the employment of quantum operators to describe the behavior of the experience in terms of probabilities. We illustrate the application of this theory through a quantitative analysis of the time evolution of the experience.
The goal of this paper is the presentation of the elementary procedures that normally are done in nonrelativistic Quantum Mechanics in terms of the principles of Machine Learning. In essence, this paper discusses Mitchell’s criteria, whose block fundamental dictates that the universal evolution of any system is composed by three fundamental steps: (i) Task, (ii) Performance and (iii) Experience. In this paper, the quantum mechanics formalism reflected on the usage of evolution operator and Green’s function are assumed to be part of mechanisms that are inherently engaged to the Machine Learning philosophy. The action for measuring observables through experiments and the intrinsic apparition of statistical or systematic errors are discussed in terms of “quantum learning”.
Among several tasks in Machine Learning, is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of such problem is the task of inferring the Hidden Markov Model underlying a given stochastic process. This is known as the positive realization problem (PRP) [Benvenuti,Farina(2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory [Luenberger(1979)]. We consider the scenario where the latent variables are quantum (e.g., quantum states of a finite-dimensional system), and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument-if any-yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the Hidden Markov Model, or the iterated quantum instrument, is however devoid from any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The Completely-Positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [Guta(2011), Guta&Yamamoto(2013)].
Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].
Quantum machine learning is an emerging Technology that is evolving rapidly and aims to translate classical machine learning models into a quantum context to be extended with the properties and applications of quantum mechanics. Despite the obvious advantage of being able to process large amounts of data in a short time, this integration between quantum and machine learning is not without challenges, especially when it comes to real datasets. In this paper, we aim to analyze the practical applicability of quantum machine learning approaches and to perform different experiments on generated and dedicated datasets that respect the quantum kernel training pattern, respectively, on real datasets, and to determine whether these can be processed to be suitable for quantum operations. To fully see the performance and potential advantage brought by the quantum component, a series of tests will be performed on both simulators and real hardware and it remains to be seen whether there is an improvement related to time complexity. Another goal based on the experiments carried out is to see on which types of datasets it is worth or justifiable to use quantum hardware at the expense of classical one. The novelty of this work lies in the use of a real-world dataset, and the experiments demonstrate that integrating quantum methods with classical processing yields higher accuracy compared to purely classical approaches.