User:Afk2231/Quantum machine learning

Quantum machine learning is the integration of quantum algorithms within machine learning programs. The most common use of the term refers to machine learning algorithms for the analysis of classical data executed on a quantum computer, i.e. quantum-enhanced machine learning. While machine learning algorithms are used to compute immense quantities of data, quantum machine learning utilizes qubits and quantum operations or specialized quantum systems to improve computational speed and data storage done by algorithms in a program. This includes hybrid methods that involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster on a quantum computer. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. Beyond quantum computing, the term "quantum machine learning" is also associated with classical machine learning methods applied to data generated from quantum experiments (i.e. machine learning of quantum systems), such as learning the phase transitions of a quantum system or creating new quantum experiments. Quantum machine learning also extends to a branch of research that explores methodological and structural similarities between certain physical systems and learning systems, in particular neural networks. For example, some mathematical and numerical techniques from quantum physics are applicable to classical deep learning and vice versa. Finally, researchers investigate more abstract notions of learning theory with respect to quantum information, sometimes referred to as "quantum learning theory".

Four different approaches to combine the disciplines of quantum computing and machine learning. The first letter refers to whether the system under study is classical or quantum, while the second letter defines whether a classical or quantum information processing device is used.

Machine learning with quantum computers

Quantum machine learning algorithms based on Grover search

Another approach to improving classical machine learning with quantum information processing uses amplitude amplification methods based on Grover's search algorithm, which has been shown to solve unstructured search problems with a quadratic speedup compared to classical algorithms. These quantum routines can be employed for learning algorithms that translate into an unstructured search task, as can be done, for instance, in the case of the k-medians and the k-nearest neighbors algorithms. Another application is a quadratic speedup in the training of perceptron.

An example of amplitude amplification being used in a machine learning algorithm is Grover's search algorithm minimization. In which a subroutine uses Grover's search algorithm to find an element less than some less than some previously defined element. This can be done with an oracle that determines whether or not a state with a correponding element is less than the predefined one. Grover's algorithm can then find an element such that our condition is met. The minimization is initialized by some random element in our data set, and iteratively does this subroutine to find the minimum element in the data set. This minimization is notably used in quantum k-medians, and it has a speed up of at least $O({\sqrt {n/k}})$ compared to classical versions of k-medians, where $n$ is the number of data points and $k$ is the number of clusters.

Amplitude amplification is often combined with quantum walks to achieve the same quadratic speedup. Quantum walks have been proposed to enhance Google's PageRank algorithm as well as the performance of reinforcement learning agents in the projective simulation framework.

Quantum machine learning skepticism

While Machine Learning itself is now not only a research field but an economically significant and fast growing industry and Quantum Computing is a well established field of both theoretical and experimental research, Quantum Machine Learning remains a purely theoretical field of studies. Attempts to prove experimentally concepts of Quantum Machine Learning remain rear and insufficient.

Many of the leading scientists that extensively publish in the field of Quantum Machine Learning beware about the extensive hype around the topic and are very restrained if ever speaking about any practical use of it in a foreseen future. Sophia Chen collected some of the statements made by well known scientists in the field:

• "I think we haven't done our homework yet. This is an extremely new scientific field," - physicist Maria Schuld of Canada-based quantum computing startup Xanadu.
• "There is a lot more work that needs to be done before claiming quantum machine learning will actually work," - computer scientist Iordanis Kerenidis, the head of quantum algorithms at the Silicon Valley-based quantum computing startup QC Ware.

• "I have not seen a single piece of evidence that there exists a meaningful [machine learning] task for which it would make sense to use a quantum computer and not a classical computer," - physicist Ryan Sweke of the Free University of Berlin in Germany.

“Don’t fall for the hype!” -  Frank Zickert, who is the author of probably the most practical book related to the subject beware that ”quantum computers are far away from advancing machine learning for their representation ability”, and even speaking about evaluation and optimization for any kind of useful task quantum supremacy is not yet achieved. Furthermore, nobody among the active researchers in the field make any forecasts about when it could possibly become practical.