QElephant

QElephant is a small library without pretention. It simulates the behavior of a quantum computer. The syntaxe is simple and can be used in any code in Python.

Installation

You can install the latest version of QElephant with :

pip install QElephant

Dependencies

In order to work, QElephant is using the following libraries:

• math
• random

They are automatically managed when installing QElephant.

Contains

This library contains two main object : QuBit and Matrix.

QuBit

This is the specificity of a quantum algorithm: using QuBit which can have two states: |0> and |1>. To create one, simply use:

q = QuBit(alpha, beta)

\alpha and \beta are optional complex arguments. When specified, initiate the QuBit in the state \alpha |0> + \beta |1>.

Important

Because the value of \alpha and \beta gives the probability of each states, it is essential that |\alpha|²+|\beta|²=1. On the other case, the QuBit cannot be created.

To simulate intricated QuBit, MuBit are used. As for QuBit, they are initalized like this:

mq = MuBit(n)
q = mq[0]

n gives the number of intricated QuBit. When created, a MuBit is in the state with only zeros.

mq[0] returns a QuBit, here the first one, wich can be manipulated. Because of the intrication, manipulating a intricated QuBit implies that other QuBits are manipulated too.

Matrix

Matrix are used to manipulate the state of the QuBit. For example, the QuBit

\alpha |0> + \beta |1>

is represented by

\begin{pmatrix}
\alpha\\
\beta
\end{pmatrix}

So, the operation corresponding of the inversion of the value of \alpha and \beta is

\begin{pmatrix}
0 & 1\\
1 & 0
\end{pmatrix}
\times
\begin{pmatrix}
\alpha\\
\beta
\end{pmatrix}
=\begin{pmatrix}
\beta\\
\alpha
\end{pmatrix}

In theory, the users don't need to use them, the main quantum gates are already implemented.

Quantum Gate

The quantum gates are the different operations applying to the QuBits. The one behind is the gate X. It is simply used like any function:

# a QuBit is created
q = QuBit() 

# the values of the QuBit are inverted
X(q)

# q is now in the state 0 |0> + 1 |1>

the complete list can be find in the docs.

Some gates need a MuBit in entry. This is the case for the controlled gate. In such a case, multiple QuBit are manipulated at the same time. The following QuBit must be specified:

mq = Mubit(2)
# in the state |00>

X(mq[0])
# now in the state |10>

SWAP(mq, 0, 1)
# the two first quibit are inverted, mq is finally in the state |01>

Docs

A doc is availaibale here where all objects and gates are displayed.

Others

Warning

Because this library is only a simulation of a qantum computer, lot of calculus are made. Manipulating n intricated qubits means manipulating matrices of size 2^n. So, it demandes much more time to calvulate than a real qantum computer.