# Variational Quantum Circuits for Machine Learning.
###### Abstract  
Quantum computing is a new paradigm for a multitude of computing applications. This study presents the technologies that are currently available for the physical implementation of qubits and quantum gates, establishing their main advantages and disadvantages and the available frameworks for programming and implementing quantum circuits. One of the main applications for quantum computing is the development of new algorithms for machine learning. In this study, an implementation of a quantum circuit based on support vector machines (SVMs) is described for the resolution of classification problems. This circuit is specially designed for the noisy intermediate-scale quantum (NISQ) computers that are currently available. As an experiment, the circuit is tested on a real quantum computer based on superconducting qubits for an application to detect weak signals of the future. Weak signals are indicators of incipient changes that will have a future impact. Even for experts, the detection of these events is complicated since it is too early to predict this impact. The data obtained with the experiment shows promising results but also confirms that ongoing technological development is still required to take full advantage of quantum computing. quantum computing; variational quantum circuits; quantum support vector machines; weak signals of the future; machine learning +
Footnote †: journal: Applied Sciences  
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<ccs2021> <concept>  
quantum systems. The machine evolved in steps. At the end of each step, the tape was always in a fundamental state of '1' or '0'. However, during each step, the machine could be in a superposition of spin states. Soon after the first idea for a quantum computer, some scholars [5] introduced the'speculative' idea that a computer based on the laws of quantum mechanics could perform complex calculations faster than conventional binary computers. Conventional computers convert data into a series of binary digits called bits that constitute the basic units of information. These bits can only have the values of '0' and '1' and are encoded in integrated circuits according to electrical signals of different voltages. Technological advancements have enabled the creation of devices that act as bits. Today an integrated circuit contains millions and millions of transistors. In contrast, data processed by quantum computers use 'qubits' that can have the value of '0' and '1' at the same time. Unlike bits, qubits can be in a superposition of both states [6]. The Bloch sphere [7] is a geometrical representation of all possible superposition states that a qubit can adopt, as can be seen in Figure 1a. Each point on the surface of the sphere corresponds to a pure state of the Hilbert space of complex dimension 2. The point of coordinates (0,0,1) corresponds to an eigenvector with a positive eigenvalue of the Pauli matrix and the point of coordinates (0,0,\(-\)1) corresponds to the eigenvector with negative eigenvalue. Both states are expressed with the notation \(\,10\)\(>\) and \(\,11\)\(>\) and correspond to spin up and spin down. The qubit can be represented as a linear combination of both states, as shown in the equation, where a and b are complex numbers, and where \(\,|\,\alpha\,|^{2}+\,|\,\beta\,|^{2}=1\). \[|\,\psi\rangle=\alpha|0\rangle+\beta|\,1\rangle=r_{a}e^{i\phi_{a}}|0\rangle+r_ {\beta}e^{i\phi_{\beta}}|1\rangle \tag{1}\]  
The Bloch sphere makes it possible to visualize the action of different quantum gates graphically. For example, one of the most used quantum gates is the Hadamard gate that operates on a single qubit. This gate is equivalent to the combination of two rotations, one of pi about the z-axis followed by a rotation of pi/2 about the y-axis of the Bloch sphere as shown in Figure 1b. The Hadamard gate is the 'quantum Fourier transform' performed on a qubit [8]. The Hadamard gate is usually the first stage in a quantum circuit because it places the qubit in a state of superposition.