I am now developing a Mathematica package that implements common tools and notations used in quantum information. The package currently includes 250+ functions and consists of 4500+ lines of Mathematica code. I continually add to this package as my research progresses, and it will be publicly available at a later point during my Ph.D. Functionality includes but is not limited to :
- Hamiltonian description of systems of coupled superconducting qubits of arbitrary connectivity and their external controls.
- Simulation of arbitrary quantum systems with external controls in open or closed quantum system contexts.
- Implementation of Hilbert spaces and Bra-Ket notation for arbitrary numbers of qubits.
- Simulation and plotting of quantum circuits by individual gate specification.
- Evaluation of quantities related to local equivalence in SU(4).
- Implementation of Kraus operators and maps on quantum systems, as well as functions related to fidelity, Shannon/Von Neumann entropy (standard, relative, conditional), information, etc.
- Functions to help with visualization, e.g. Bloch sphere plotting, generation of figures for quantum circuits, etc.
Quantum Fourier Transform
As an undergraduate, I worked on implementing the quantum Fourier transform on a specific architecture of quantum computing. Below are some slides explaining what I did, and why I think it is important.
Algebraic Graph Theory
As an undergraduate, I took a research math class focused on algebraic graph theory taught by Dr. Dino Lorenzini. We looked at the Smith Normal Form of certain families of graphs, and made conjectures about their properties. The results of this work and supporting code are available on GitHub.