106 lines
No EOL
2.6 KiB
Markdown
106 lines
No EOL
2.6 KiB
Markdown
# QElephant
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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.
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## Installation
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You can install the latest version of QElephant with :
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```
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pip install QElephant
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```
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## Dependencies
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In order to work, QElephant is using the following libraries:
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- `math`
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- `random`
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They are automatically managed when installing QElephant.
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## Contains
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This library contains two main object : `QuBit` and `Matrix`.
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### QuBit
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This is the specificity of a quantum algorithm: using QuBit which can have two states: `|0>` and `|1>`. To create one, simply use:
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```
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q = QuBit(alpha, beta)
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```
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$\alpha$ and $\beta$ are optional complex arguments. When specified, initiate the QuBit in the state $\alpha$ |0> + $\beta$ |1>.
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> [!IMPORTANT]
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> 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.
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To simulate intricated QuBit, `MuBit` are used. As for `QuBit`, they are initalized like this:
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```
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mq = MuBit(n)
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q = mq[0]
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```
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`n` gives the number of intricated QuBit. When created, a MuBit is in the state with only zeros.
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`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.
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### Matrix
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`Matrix` are used to manipulate the state of the QuBit. For example, the QuBit
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$\alpha$ |0> + $\beta$ |1>
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is represented by
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$\begin{pmatrix}
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\alpha\\
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\beta
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\end{pmatrix}$
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So, the operation corresponding of the inversion of the value of $\alpha$ and $\beta$ is
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$\begin{pmatrix}
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0 & 1\\
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1 & 0
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\end{pmatrix}
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\times
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\begin{pmatrix}
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\alpha\\
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\beta
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\end{pmatrix}
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=\begin{pmatrix}
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\beta\\
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\alpha
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\end{pmatrix}$
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In theory, the users don't need to use them, the main quantum gates are already implemented.
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### Quantum Gate
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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:
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```
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# a QuBit is created
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q = QuBit()
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# the values of the QuBit are inverted
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X(q)
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# q is now in the state 0 |0> + 1 |1>
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```
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the complete list can be find in the [docs](docs).
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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:
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```
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mq = Mubit(2)
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# in the state |00>
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X(mq[0])
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# now in the state |10>
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SWAP(mq, 0, 1)
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# the two first quibit are inverted, mq is finally in the state |01>
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```
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## Docs
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A doc is availaibale [here](docs) where all objects and gates are displayed. |