Quantum Support Vector Machines QSVM - RPIQuantumComputing/QuantumCircuits GitHub Wiki

Quantum machine learning is an extension from the classical machine learning in order to go beyond the limits of classical computing by combining machine learning with the unique properties of quantum mechanics. Its objective is to aim at solving complex Machine learning problems more effectively and more efficiently than classical Machines, it utilizes ideas of superposition, entanglement, interference, and etc. to solve problems, particularly those with enormous amounts of data, that classical machines cannot solve in a reasonable amount of time.

One of the most prominent algorithms of quantum machine learning includes Quantum Support Vector Machines or QSVM, is a quantum version of classical support vector algorithm. A support vector algorithm is an algorithm designed to be used in linear or nonlinear data classification, regression, and outlier detection, it is commonly used in text classification, image classification, spam detection, handwriting detection, anomaly detection, and etc. It basically finds an optimal hyperplane, plane whose number of dimension is one less than its ambient space, and uses it to separate the data points into different classes by maximizing the difference the difference between them, basically think about it as drawing an optimal line to separate individual groups of objects. For larger datasets it is near impossible to segregate the different classes optimally using linear lines, so non-linear lines are required, in these cases, we use a kernel trick to push each classes into another dimension where a hyperplane could be defined. However, this method has a downside, as the size of the dataset or more broadly speaking, the size of the input increases, the computational complexity will increases at an extreme rate making the algorithm worthless when put to use on user large data.

Quantum support vector machine sidesteps this issue by implementing quantum mechanics to limit the run time. It basically operates on the same principle as classical support vector machine but uses quantum devices to perform the optimization and finding the hyperplane. The QSVM optimizes a function of the sum of the squares of the distance between each data point and the hyperplane, and the hyperplane is found when we have the maximum value after optimization. The optimization method can be any optimization method depending on the size of the dataset or the input, one example would be the quantum gradient descent algorithm, which iterates the parameters of the machine learning model in the direction of the steepest descent in order to find the optimized hyperplane. When compared with classical support vector machine, quantum support vector machines are much faster because classical computers cannot grow the size of the domains to match the demand from the algorithm while its quantum counterpart can, in order to access an extremely high dimension using the kernel trick from a classical machine, it will have to sacrifice resolution and speed to only estimate the optimal hyperplane that the user wants.

Some of the advantages of Quantum Vector Support Machines over the classical vector support machine include having a faster training time through the increased computational power of the quantum machine, useful for large scale machine learning tasks that could take some time for a classical machine to complete. Another advantage is its ability to access higher dimensions for mapping, as QVSM can access higher dimensions that a classical computer cannot which creates more accurate separation of data points compared to a classic kernel. However, quantum machines still has its disadvantages and problems that needs to be resolved, QVSM is not universally better than classical problems, only in specific cases is it better, and while in theory quantum machine learning is more advantageous in data certain areas such as going through data sets of data or factoring an extremely large number, it is still actively being researched and developed as of today.