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Classical machine learning, which is at the intersection of artificial intelligence and statistics, investigates and formulates algorithms which can be used to discover patterns in the given data and also make some forecasts based on the given data. Classical machine learning has its quantum part, which is known as quantum machine learning (QML). QML, which is a field of quantum computing, uses some of the quantum mechanical principles and concepts which include superposition, entanglement and quantum adiabatic theorem to assess the data and make some forecasts based on the data. At the present moment, research in QML has taken two main approaches. The first approach involves implementing the computationally expensive subroutines of classical machine learning algorithms on a quantum computer. The second approach concerns using classical machine learning algorithms on a quantum information, to speed up performance of the algorithms. The work presented in this manuscript proposes a quantum support vector algorithm that can be used to forecast solar irradiation. The novelty of this work is in using quantum mechanical principles for application in machine learning. Python programming language was used to simulate the performance of the proposed algorithm on a classical computer. Simulation results that were obtained show the usefulness of this algorithm for predicting solar irradiation.

Machine learning is a subfield of artificial intelligence. It is a set of techniques that are used to analyze and find patterns in input data to make predictions/inferences [

There are various classical machine learning algorithms, and these include Bayesian networks, artificial neural networks, deep learning, clustering and Support Vector Machine (SVM) to name but a few. The main focus of this paper is on the quantum version of SVM algorithm, which was introduced by Vapnik in the 1990s [

The field of Quantum Information Processing (QIP) exploits quantum mechanical concepts such as superposition, entanglement and tunneling for computation and communication tasks [

There are two basic approaches to QML [

The remainder of this paper is structured as follows. The next section provides background information on machine learning, QIP and QML. This is followed by Section 3, which discusses the design and implementation of the sun power prediction model reported in this Manuscript. Section 4 provides the results and discusses the results obtained. Finally, the last section concludes this paper.

Machine learning, which is used interchangeably with predictive analytics, is a sub-field of artificial intelligence which is concerned with building algorithms that make use of input data to make predictions [

-Supervised learning: makes use of both training data and data label to make predictions about future points. Examples of supervised learning algorithms are logistic regression, artificial neural networks and support vector machines.

-Unsupervised learning: makes use of training data only to make a model that maps inputs to output. As opposed to supervised learning, unsupervised learning does not make use of data label. Examples of unsupervised learning are clustering and anomaly detection algorithms.

-Reinforcement learning: uses reinforcement in the form of reward or punishment. If the algorithm succeeds in making correct predictions, it is rewarded. However, if it fails, it is punished. Reinforcement learning is used mainly in robotics and computer games.

Support vector machine learning is the most commonly used “off-the-shelf” supervised learning algorithm [

One of the key advantages of support vector machines is that unlike other supervised learning algorithms, its loss function is a global optimization problem, hence it is not prone to local optima [

In stark contrast to classical computers, which use a binary digit (bit) as a unit of information, quantum computers use a quantum bit (qubit) as a unit of information. Mathematically, a qubit is given as [

where α and β are probability amplitudes. These amplitudes satisfy the condition

It is worth noting that a qubit, which is a unit of information for a two-state system, can be generalized to any arbitrary d-state. Such a generalized unit of information is known as a quantum digit (qudit) [

Machine learning generally represents data in vector and matrix form. This is also the case with QIP, hence why QIP concepts find applications in machine learning. This results in the new field of research called quantum machine learning. Quantum machine learning can take two forms: where classical machine learning algorithms are transformed into their quantum counterparts; to be implemented on a quantum information processor, or taking some of the computationally expensive classical machine learning sub-routines and implementing them on the quantum computer.

Different measures are used to evaluate and validate models. These measures include mean squared error (MSE), Root mean squared error (RMSE), mean absolute error (MAE), and R^{2} error.

Mean squared error is one of the measures of the goodness of fit. It measures the closeness of a data line to the data points. For n as the number of predictions,

Root mean squared error, which is also a measure of goodness of fit, is the average Euclidean distance of the line from the data points. It is given as

where n is the number of predictions,

Mean absolute error measures the closeness of predicted results to the observations. It is given as

R^{2} error is also known as coefficient of determination. It is the measure of degree of variance. It is given as

where, for a mean of observations

and

In this work, quantum support vector machine was implemented using a recorded data from Digital Technology Group (DTG) Weather Station in Cambridge University^{1}. The dataset consists of forty nine instances, which are the training examples. These instances represent the measurements that were recorded at DTG, with a time interval of thirty minutes. Additionally, this dataset consists of three features, namely temperature, humidity and wind speed.

The recorded classical information is converted to quantum state such that for a training example

This is then followed by optimizing the quantum support vector hyperplane parameters, as articulated in [

The quantum support vector machine was implemented using Python programming language.

Python machine learning package used for this task was Scikit-learn version 0.18.0 [^{2}. This GUI helped visualize the input dataset and the plots for the results obtained from this implementation. It also supports other python packages such as scikit-learn.

The results were then recorded and errors calculated. The following errors were calculated, for different training sizes:

_mean square error (MSE),

_root mean square error (RMSE),

_mean absolute error (MAE),

_coefficient of determination, R^{2}.

The dataset was broken down into different portions, with some part being used for training data, and the other part being used for cross-validation.

The next step was to analyze the correlation of the three features used (temperature, humidity and wind speed).

We have reported an algorithm for solar power prediction using quantum support vector machine learning algorithm. The algorithm is a quantum counterpart of a classical support vector machine, which is known to have a unique solution, and hence it converges

Training Size (%) | MSE | RMSE | MAE | R^{2 } |
---|---|---|---|---|

60 | 3.629 | 1.905 | 1.435 | 0.978 |

66 | 3.098 | 1.760 | 1.283 | 0.826 |

70 | 2.643 | 1.626 | 1.171 | 0.852 |

75 | 2.992 | 1.730 | 1.259 | 0.835 |

80 | 3.014 | 1.736 | 1.257 | 0.835 |

to a global optimum. This is in contrast to other machine learning algorithms such as neural networks, which can converge to local optima, since they may not have unique solutions.

In the work reported in this paper, the quantum support vector algorithm was simulated using Python programming language. A dataset with forty nine instances and three features (temperature, humidity and windspeed) was used for this simulation. The results obtained from the simulation underline the utility of the proposed quantum support vector algorithm for solar power prediction. However, it should be noted that in the implementation, a generic optimization algorithm was used for implementing quantum SVM. Future work should explore the feasibility.

Senekane, M. and Taele, B.M. (2016) Prediction of Solar Irradiation Using Quantum Support Vector Machine Learning Algorithm. Smart Grid and Renewable Energy, 7, 293-301. http://dx.doi.org/10.4236/sgre.2016.712022