Introduction to Quantum Machine Learning

"Biggest question of all time 'Will machines take over humans in every task?' Only time will tell the answer!"

In Quantum Computing, the number of possible states is described by the number of possible qubits. The number of possible quantum states is 2 to the power of the number of qubits. If we consider this relation, then with just 275 qubits we can represent more states than the number of atoms in the observable universe. ML models made on quantum computing may be incredibly powerful for some applications allowing for faster computation and better generalization on less data.

A mathematical concept called Hilbert Space(Infinite-dimensional space) generalizes the notion of Euclidean Space(Finite-dimensional space). This extends the methods of vector algebra and calculus. A Hilbert Space processes the structure of inner products that allow the length and angle to be measured. Hilbert Spaces are complete so there are enough limits in space to allow for calculus to be used and it's just a massive space that allows for all this quantum advantage to be possible.

Types of Machine Learning:

• CC: Classical data processed by Classical Machine Learning Algorithm

• CQ: Classical data processing by Quantum Machine Learning Algorithm

• QC: Quantum data processing by Classical Machine Learning Algorithm

• QQ: Quantum data processing by Quantum Machine Learning Algorithm

CQ is where most of the research goes on as it involves developing a Quantum Algorithm.

QC is an area of investigation with Classical ML algorithms being used to process quantum data such as control readout and qubit characterization.

QQ is a fully quantum and a big active area of development.

A lot of research focuses on creating algorithms for Universal Quantum Computing that are fault-tolerant. There are several algorithms developed for noisy quantum devices which are near-term devices.

Advantages of Quantum Machine Learning:

• Solving Linear Algebraic Problems

• Reinforcement Learning

• Dimensionality Reduction

• Introduce some speed up in the above operations

In quantum computing, a quantum state of qubits is a vector in a 2^n dimensional complex vector space and in this space, a lot of matrix transformation happens which can be quite taxing. QML algorithms are based on amplitude encoding i.e. associating amplitudes of quantum state with the inputs. Since qubits can describe 2^n amplitudes, this information encoding can allow for exponentially compact representation. There are several ways that quantum properties can help to enhance classical algorithms to speed up computation. E.g. If a data set has a million features the classical methods such as PCA(Principle Component Analysis) to reduce the dimensionality will be difficult or fail as it's hard to visualize the importance of each variable.

Another issue is that the classical computers struggle with calculation of eigenvectors and eigenvalues in higher dimensionality as higher the number of dimensions the larger the set of corresponding eigenvectors and eigenvalues. So this is the issue that quantum computing can solve very efficiently at high speeds due to QRAM. It maps the vectors to quantum states using qubits. This reduces computational complexity and time complexity.

Qiskit Machine Learning introduces fundamental computational building blocks such as quantum kernels and quantum neural network which can be applied to many different applications. These QML models can run on Qiskit simulators as well as real quantum devices.

To explore more on qiskit machine learning check this github repository:

https://github.com/qiskit-community/qiskit-machine-learning

Thank you IBM, Desiree Vogt Lee for such an amazing introductory session to Quantum Machine Learning in Quantum Explorer's 2023.