QuantumDots.jl

This package provides some tools for working with quantum systems. The scope is not clearly defined and the api may change. As such, the package is not registered in the general registry but can be installed by

using Pkg; Pkg.add(url="https://github.com/cvsvensson/QuantumDots.jl")

Functionality includes

• Many-body fermionic systems (with support for conserved quantum numbers)
• Free fermionic systems
• Qubit systems
• Open system dynamics: Lindblad and Pauli

Introduction

Let's analyze a small fermionic system. We first define a basis

using QuantumDots
N = 2 # number of fermions
spatial_labels = 1:N 
internal_labels = (:↑,:↓)
c = FermionBasis(spatial_labels, internal_labels)

Indexing into the basis like returns sparse representations of the fermionic operators, so that one can write down Hamiltonians in a natural way

H_hopping = c[1,:↑]'c[2,:↑] + c[1,:↓]'c[2,:↓] + hc 
H_coulomb = sum(c[n,:↑]'c[n,:↑]c[n,:↓]'c[n,:↓] for n in spatial_labels)
H = H_hopping + H_coulomb
#= 16×16 SparseArrays.SparseMatrixCSC{Int64, Int64} with 23 stored entries:
⎡⠠⠂⠀⠀⠀⠀⠀⠀⎤
⎢⠀⠀⠰⢂⠑⢄⠀⠀⎥
⎢⠀⠀⠑⢄⠠⢆⠀⠀⎥
⎣⠀⠀⠀⠀⠀⠀⠰⢆⎦ =#

One can also work in the single particle basis FermionBdGBasis if the system is noninteracting. Quadratic functions of the fermionic operators produce the single particle BdG Hamiltonian.

c2 = FermionBdGBasis(spatial_labels, internal_labels)
Hfree = c2[1,:↑]'c2[2,:↑] + c2[1,:↓]'c2[2,:↓] + hc
vals, vecs = diagonalize(BdGMatrix(Hfree)) 

Using diagonalize on a matrix of type BdGMatrix enforces particle-hole symmetry for the eigenvectors.

More info

• For a more in depth introduction see pmm_notebook.

• QubitBasis and time evolution is demonstrated in qubit_dephasing.

• Simulation of Majorana braiding demonstrated in majorana_braiding and majorana_braiding_noisy.

• Most functionalities of the package are demonstrated in the tests.