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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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Supervised learning with quantum-enhanced feature spaces.

Vojtěch Havlíček1,2, Antonio D Córcoles3, Kristan Temme4

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Summary
This summary is machine-generated.

This study introduces two quantum algorithms for machine learning classification, leveraging quantum computing's potential to overcome limitations in large feature spaces and computationally expensive kernel estimations for support vector machines (SVMs). These methods utilize quantum state spaces for enhanced feature representation, paving the way for quantum advantage in machine learning tasks.

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Area of Science:

  • Quantum Computing
  • Machine Learning
  • Supervised Learning

Background:

  • Kernel methods in machine learning, such as support vector machines (SVMs), face challenges with large feature spaces and computationally expensive kernel function estimations.
  • Quantum computing offers potential computational speed-ups by exploiting exponentially large quantum state spaces through entanglement and interference.
  • Bridging quantum computing and machine learning is crucial for addressing complex computational problems.

Purpose of the Study:

  • To propose and experimentally implement two novel quantum algorithms for supervised learning classification tasks.
  • To explore the use of quantum-enhanced feature spaces for potential quantum advantage in machine learning.
  • To investigate the application of noisy intermediate-scale quantum (NISQ) computers to machine learning.

Main Methods:

  • Experimental implementation of two quantum algorithms on a superconducting processor.
  • Utilizing the quantum state space as an enhanced feature space, accessible efficiently only on a quantum computer.
  • One method employs a quantum variational classifier using variational quantum circuits, analogous to classical SVMs.
  • The second method involves a quantum kernel estimator that computes kernel functions on the quantum computer to optimize a classical SVM.

Main Results:

  • Successful experimental implementation of two quantum algorithms for classification.
  • Demonstration of quantum-enhanced feature spaces as a pathway to quantum advantage.
  • Development of tools for applying NISQ devices to machine learning problems.

Conclusions:

  • Quantum algorithms can effectively address limitations in classical machine learning, particularly for large feature spaces.
  • Quantum-enhanced feature spaces offer a promising approach for achieving quantum advantage in machine learning.
  • The developed methods provide practical tools for leveraging NISQ computers in machine learning applications.