HOME

Hamiltonian Open Quantum System Toolkit (HOQST) for the Julia programming language.

The official name of this package is "Hamiltonian Open Quantum System Toolkit" (HOQST). To conform with the Julia package name guidelines the code name of the package is OpenQuantumTools.

Installation

To install, run the following commands inside the Julia REPL:

using Pkg
Pkg.add("OpenQuantumTools")

Alternatively, this can also be done in Julia's Pkg REPL:

(1.5) pkg> add OpenQuantumTools

More information about Julia's package manager can be found at Pkg.jl. OpenQuantumTools requires Julia 1.4 or higher. Installing it on an older version of Julia will result in an unsatisfiable requirements error.

To load the package, use the command:

using OpenQuantumTools

It is highly recommended that new users start with the introductory-level tutorials in HOQSTTutorials.

Useful Packages

The following external packages are needed to take full advantage of OpenQuantumTools:

DifferentialEquations.jl

DifferentialEquations is needed to provide the low-level ODE solvers. For low dependency usage, users can use OrdinaryDiffEq.jl instead.

Plots.jl

Plots is a visualization interface and toolset for Julia. OpenQuantumTools provides several plotting functionality by defining PlotRecipes.

Quick Start

In the first example, we consider a single qubit with the following time-dependent Hamiltonian

\[ H(s) = A(s)X + B(s)Z \ ,\]

which is known as a standard single qubit annealing protocol. $s$ in the above equation is the dimensionless time $s=t/t_f$ where $t_f$ means the total evolution time. $A(s)=1-s$ and $B(s)=s$ are scalar functions that are known as the annealing schedules. $X$ and $Z$ stand for the Pauli matrices $\sigma_x$ and $\sigma_z$.

The general workflow is:

1. define the Hamiltonian;
2. construct the annealing/time evolution process;
3. call the solver.

The full code for solving the Schrodinger evolution is:

using OpenQuantumTools
using DifferentialEquations
tf = 20
u0 = PauliVec[1][2]
H = DenseHamiltonian([(s)->1-s, (s)->s], [σx, σz], unit=:ħ)
annealing = Annealing(H, u0)
sol = solve_schrodinger(annealing, tf)

where the different pieces are explained below.

First, we need to load the package DifferentialEquations for the ODE solvers. Then we define the Hamiltonian of the annealing process. In "OpenQuantumTools", a time-dependent Hamiltonian can be specified by a list of time-dependent functions and a list of constant matrices

H = DenseHamiltonian([(s)->1-s, (s)->s], [σx, σz], unit=:ħ)

The resulting Hamiltonian is an affine combination of the corresponding functions and the matrices $(1-s)X+ sZ$. Next, we define the initial state u0:

u0 = PauliVec[1][2]

where PauliVec is a Constant which holds the eigenvectors of the Pauli matrices. The user can define any length 2 Vector as the initial state.

An annealing/evolution object can be constructed by combining the Hamiltonian and the initial state:

annealing = Annealing(H, u0)

The final step is to call the solver. In this example, solve_schrodinger solves the Schrodinger equation for a total evolution time tf.

Tutorials

The following tutorials will introduce you to the functionality of OpenQuantumTools. More examples can be found in HOQSTTutorials.jl.