quantum

This an evolving repository of codes and notebooks that I make to learn and explore topics in solid-state physics, quantum many-body theory, information, and computation.

Contents

notebooks

• Simulation of quantum period finding algorithm.
• Numerical accuracy of the time ordered exponential for a 2-level harmonically driven system.
• Tight-binding bandstructure of 2D materials.
• Band inversion in a 2-state model.
• Tight binding band structure calculations for sp³ bonded semiconductors.

primitives

• Sherrington-Kirkpatrick model implementing an approximate optimization algorithm.
• Functions to compute continued fraction representation of a real number and vice versa.
• Decomposition of arbitrary unitary matrix into a product of $2\times2$ unitaries: qprimitives.matrixutils.
• Class for constructing operator representations in computational basis of $n$ qubits: qprimitives.toric.
• Period finding algorithm.
• Shor's factorization algorithm.

floquet

The module floquet.dyanmics implements the follwing functions:

• Matrix exponentials, $e^{a H}$, to construct unitary evolution operators.
• Construction of the Bloch-Pierels Hamiltonian with a harmonic vector potential.
• Direct time evolution from a periodically driven Hamiltonian by Suzuki-Trotter algorithm.
• Creation of Hamiltonian over the Bloch-Floquet upto 4th order block diagonalization.
• Computation of stroboscopic energy spectrum of a periodically driven Hamiltonian.

tbm

Zinc-Blende and Diamond strucutre tight binding models for sp³ bonded semiconductors: tbm.tbzincblende

• Implementation from the textbook by Yu and Cardona along with the parameters of C, Si, and Ge from Chapter 2 [1].
• 10-band model with anti-bonding s-orbitals, presented in the seminal paper by Vogl et al. [2].
• Text file with the parameter table from [2].

Tight binding models for two-dimensional materials: tbm.tbtmdc.

• Parameters for the tight binding model of MoS₂,MoSe₂,WS₂,and WSe₂ proposed in [3]
• Tight-binding Hamiltonian of Fang et. al. decomposed by hopping vectors, so that it can be put into Bloch-Pierels form for Floquet dynamics.

utils

Plotting utilities.

References

[1] Yu, Peter and Manuel Cardona, "Fundamentals of Semiconductors"

[2] Vogl, P and Hjalmarson, H and Dow, J "A SEMI-EMPIRICAL TIGHT-BINDING THEORY OF THE ELECTRONIC STRUCTURE" , I. Phys. Chom. Solids Vol. 44, No. 5. pp. 365-378, 1983. Download

[3] Fang, S., Kuate Defo, R., Shirodkar, S. N., Lieu, S., Tritsaris, G. A., & Kaxiras, E. (2015). Ab initio tight-binding Hamiltonian for transition metal dichalcogenides. Physical Review B, 92 (20). https://doi.org/10.1103/PhysRevB.92.205108