Recent Progress in Quantum Computational Complexity

John Watrous

Sanjay Singh, Ashish Mani, Rashmi Jain

Image processing plays a crucial role in our day to day life as it is helpful to solve important problems in real world. Recent progress in quantum information and computation led to the birth of a new field called Quantum Image Processing. This new field of image processing in quantum domain focuses on the development of the quantum image processing algorithms, which can run more efficiently on quantum computer. These quantum algorithms are better in terms of Image storage and retrieval with reduced computational complexity. In this article we present recent advancements in quantum image representation with different mathematical models and with their corresponding computational complexity.

Paul D. Townsend

Quantum cryptography represents a new paradigm for secure communications in which security is based on fundamental physical laws rather than computational complexity. Recent progress in the development of practical optical fiber-based systems will be described.

Daowen Qiu

Arit Kumar Bishwas, Ashish Mani, Vasile Palade

In recent years, Machine Learning (ML) has started to be ubiquitously applied to practically most of the human activity domains. Although traditional, or classical machine learning (CML) approaches are useful in solving many complex tasks, there are still many challenges that such approaches are facing. One issue is the limitation in the processing speed of current silicon technology based computers, which made researchers look to the underlying quantum theory principles and try to run complex quantum computing experiments. In future, in order to develop more complex artificial intelligence systems, we will have to process huge amounts of data at high speed, and the existing classical computing will probably not serve well this purpose, due to silicon technology limitations. A different technology that can handle huge volumes of data and at high speed is needed. In recent years, the progress in quantum computing research seems to provide hopeful answers to overcome the speed processing barrier. This is very important for the training of many computational intensive machine learning models. The latest advancements in quantum technology appear to be promising, which can boost the field of machine learning overall. In this chapter, we discuss the transition from classical machine learning to quantum machine learning (QML) and explore the recent progress in this domain. QML is not only associated with the development of high-performance machine learning algorithms that can run on a quantum computer with significant performance improvements but also has a very diverse meaning in other aspects. The chapter tried to touch those aspects in brief too, but the main focus is on the advancements in the field of developing machine learning algorithms that will run on a quantum computer.

Andris Ambainis