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==Introduction==
Quantum Support Vector Machine (QSVM) is a quantum algorithm that is an extension of the classical [[Support Vector Machine|Support Vector Machine (SVM)]] algorithm. It is a part of the broader field of [[Quantum Machine Learning|Quantum Machine Learning (QML)]], which combines principles of [[Quantum Computing|Quantum Computing]] and [[Machine Learning|Machine Learning]] to provide solutions to complex computational problems.

==Quantum Computing==
Quantum Computing is a field of study focused on the development and application of quantum computers. These computers use the principles of [[Quantum Mechanics|Quantum Mechanics]], such as superposition and entanglement, to perform computations. Quantum computers have the potential to solve problems that are intractable for classical computers, making them a promising technology for the future.

==Machine Learning==
Machine Learning is a subset of [[Artificial Intelligence|Artificial Intelligence (AI)]] that provides systems the ability to automatically learn and improve from experience without being explicitly programmed. It focuses on the development of computer programs that can access data and use it to learn for themselves. The process of learning begins with observations or data, such as examples, direct experience, or instruction, in order to look for patterns in data and make better decisions in the future based on the examples that we provide.

==Support Vector Machine==
The Support Vector Machine is a popular machine learning algorithm used for classification and regression analysis. It is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on.

==Quantum Support Vector Machine==
The Quantum Support Vector Machine is a quantum version of the classical SVM. It uses the principles of quantum computing to perform the computations required by the SVM algorithm. The QSVM algorithm can be implemented on a quantum computer and has the potential to provide speedups over classical SVM for certain datasets and problems.

[[Image:Detail-42003.jpg|thumb|center|A quantum computer running a Quantum Support Vector Machine algorithm.|class=only_on_mobile]]
[[Image:Detail-42004.jpg|thumb|center|A quantum computer running a Quantum Support Vector Machine algorithm.|class=only_on_desktop]]

==Working of QSVM==
The QSVM algorithm works by mapping the input data to a high-dimensional Hilbert space using a quantum feature map. This map is designed such that the inner product in this space corresponds to a kernel function in the original data space. The QSVM then finds the hyperplane in this high-dimensional space that separates the data into different classes, similar to the classical SVM.

==Advantages of QSVM==
QSVM has several advantages over classical SVM. Firstly, it can handle high-dimensional data more efficiently due to the exponential storage capacity of quantum states. Secondly, it can perform complex computations faster due to the parallelism inherent in quantum computation. Finally, it can potentially provide quantum speedups for certain kernel functions that are hard to compute classically.

==Limitations of QSVM==
Despite its advantages, QSVM also has some limitations. The main limitation is that it requires a quantum computer to run, which are currently not widely available or fully developed. Additionally, the quantum feature map used by QSVM may not always provide a quantum advantage, depending on the specific dataset and problem.

==Applications of QSVM==
QSVM can be applied to any problem that can be solved using classical SVM. This includes classification and regression problems in various fields such as bioinformatics, text and image recognition, and financial forecasting.

==Future of QSVM==
The future of QSVM is closely tied to the development of quantum computing. As quantum computers become more powerful and accessible, the use of QSVM and other quantum machine learning algorithms is expected to increase. Research is also ongoing to develop new quantum feature maps and algorithms that can provide greater quantum advantages.

==See Also==
* [[Quantum Computing]]
* [[Machine Learning]]
* [[Support Vector Machine]]
* [[Quantum Machine Learning]]
* [[Quantum Algorithms]]

[[Category:Quantum Computing]]
[[Category:Machine Learning]]
[[Category:Quantum Machine Learning]]