I will begin the lecture with an overview of recent and important developments in the area of quantum algorithms and an in-depth review of a quantum information processing proposal. As a part of the algorithms review of my presentation, I will carefully define the quantum information data structure, what types of computations are possible, and how to measure the result of a computation. While this alone suffices to formulate deeper and more interesting algorithms such as famous Shor's factoring or Grover's search, I will only illustrate one simple example where a quantum algorithm is provably more efficient than a classical one. The second part of my review is introduction of a quantum information processing proposal, in particular, the liquid NMR approach. I will explain the physics and some of the engineering details behind this technology. I will conclude with a brief discussion of the achievements and limitations of liquid NMR implementations.

I will next concentrate on how the possible quantum algorithms could be systematically and efficiently implemented on quantum hardware and what may be potential difficulties in trying to do so, i.e. quantum CAD. I will introduce the following quantum CAD topics: circuit synthesis, circuit optimization, scheduling/placement, simulation, fault tolerance, and quantum architectures. I will elaborate in details on the research I have personally done in one (time permitting two) of this topics, as per audience' choice.