Keywords:
Geometric Control, Quantum Computing, BCS Superconductivity, Josephson Junctions, Google Qubit, Quantum error correction
Synopsis
Description
Efficient information processing and secure information travel are major problems faced by humans. To be able to build materials for quantum computing, I started with my project on BCS theory and high temperature superconducting materials. Surveyed literature on solid state theory including BCS theory of superconductivity and explored explanations of high temperature superconducting materials. Studying Josephson junctions and Google’s implementation of qubits for building Quantum computers. This builds on my background in topological quantum computing for which I did a course project on Kitaev Model and Majorana Fermions covering Jordan-Wigner Transforms, braiding and Non-Abelian Statistics. I will also be learning spectroscopy techniques including NMR, optimal control and error correction for quantum control of systems.
Abstract
The tremendous amount of work done in the field of superconductivity can be seen just by a quick glance at the Nobel prizes awarded to Kamerlingh Onnes for the discovery of superconductivity [1], John Bardeen, Leon Cooper and Robert Schrieffer for the microscopic (BCS) theory of superconductivity [2], Brian Josephson for the Josephson effect in superconducting junctions [3], Georg Bednorz and Alex M"uller for the discovery of high-temperature superconductivity in perovskite oxides [4], and Alexei Abrikosov, Vitali Ginzburg, and Anthony Leggett for their theories of type II superconductivity and superfluidity [5].
- Report will be up in a day or two.
Related Background work
- Undergraduate courses in Quantum Mechanics, Electronic Properties of Materials, Semiconductor Devices and Physics, Condensed Matter Physics and Electromagnetic Theory. Graduate courses: Physics of Nanostructures and Nanoscale Devices and Introduction to Nanoscience and Nanotechnology by Prof. Anshuman Kumar, Computational Many Body Physics (PH 554) by Prof. Soumya Bera and the following: Quantum Control (SC 638) by Prof. Navin Khaneja.
- Quantum Control based on SC 701, IITB by Prof. Navin Khaneja.
- Solid State Systems and Control Work out 1 based on SC 624, IITB by Prof. Navin Khaneja.
- Differential Geometry for Control Theory based on SC 624, IITB by Prof Debashish Chatterjee and TA Rayyan and help from Mishal Assif.
- Process Control and Instrumentation based on MM 401, IITB by Prof. N. K. Khosla.
- Physics and Control, Linear Systems, Quantum Control based on SC 701, IITB by Prof. Navin Khaneja.