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
• numpy

They are automatically managed when installing QElephant.

Contains

This library contains three main object : QuBit, Matrix and Circuit.

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 entangled QuBit, MuBit are used. As for QuBit, they are initalized like this:

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

n gives the number of entangled 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 entangled 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.

Circuit

A Circuit is an object contaning a MuBit. When manipulating it, it send to the Circuit a signal in order to keep in memory when a gate is used, and on which QuBit.

So, it is simply used like a MuBit :

# a Circuit with 3  entangled SuBit is created
c = Circuit(3)

# get the MuBit in this circuit
mb = c.get_MuBit()

# manipulate le MuBit
List_of_QuBit = [mb[i] for i in range(3)]

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>

Finally, a gate can be simply apply on all the QuBit of a MuBit:

mb1 = MuBit(7)
mb2 = MuBit(7)

H(mb2)

for i in range(7):
    H(mb2[i])

# at the end, the two MuBit are in the exact same state

Note

Only a single qubit gate can be apply to all the QuBit at the same time. For a Circuit, maust be apply to the QuBit, and not to the circuit

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 calculation are made. Manipulating n entangled qubits means manipulating matrices of size 2^n. So, it demandes much more time to calculate than a real qantum computer.