826 Understanding Quantum Computing

It is the aim of this course to use just graduate-level mathematical tools and terminologies to explain the concepts underlying quantum computing and the functions of the corresponding hardware—The Quantum Computer. The main differences between classical and quantum mechanics will be concisely presented. Quantum dynamic variables like position and momentum in mechanical systems as well as voltage and current in electrical circuits will be shown to behave as random rather than deterministic signals, whose attributes can be used to carry information. It will also be demonstrated that these random signals can be stored and processed in what is called Qubit. The latter is the quantum counterpart of the classical Bit. The hardware realization of qubits in form of superconducting circuits—the Transmons—will be explained in details.

Due to the impossibility of fully isolating dynamic systems from their surroundings, thermal noise and quantum dynamic variables, both being random signals, interact together. As opposed to deterministic signals, noise corruption has a different form in this case. It deteriorates an essential statistical attribute of interacting quantum dynamic variables, which is known as “Coherency”. The latter is a sort of “memory”, which enables different quantum dynamic variables to “remember” each other.

Using quantum systems for encoding and processing information needs therefore cooling the systems down to very near the absolute zero temperature (0°K) in order to reduce the noise impact on the coherency. Coding and processing errors due to deteriorated coherencies might also need involving error-correction techniques similar to those known in Channel Coding.

In addition to a detailed consideration of the concepts mentioned above, the course will review the fundamentals of a number of subjects including Probability Theory, Boolean Algebra and Binary Information Processing, Probabilistic Computation, Superconducting Transmons and Josephson Junctions, and Quantum Gates.

A minimum amount of quantum mechanical terminologies and mathematical tools will be used in this course. This should avoid the common perception that the subject of Quantum Computation is a highly sophisticated and specialized one, which needs excessive mathematical background. Only graduate level fundamental knowledge on Physics and Mathematics is needed.

In addition to a detailed consideration of the concepts mentioned above, the course will review the fundamentals of a number of subjects including Probability Theory, Boolean Algebra and Binary Information Processing, Probabilistic Computation, Superconducting Transmons and Josephson Junctions, and Quantum Gates.

A minimum amount of quantum mechanical terminologies and mathematical tools will be used in this course. This should avoid the common perception that the subject of Quantum Computation is a highly sophisticated and specialized one, which needs excessive mathematical background. Only graduate level fundamental knowledge on Physics and Mathematics is needed.

The course is dedicated to Engineers, Computer Scientists, Software Developers, Digital-Signal-Processing Specialists, and Academic Researchers. A general background in Physics and Mathematics is required.