> ## Documentation Index
> Fetch the complete documentation index at: https://prod-mint.classiq.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Classical Types

This is a list of the classical types that are built-in in `Qmod`.
For more information regarding classical types see: [classical types](../../../qmod-reference/language-reference/classical-types/).

Members:

| Name              | Description                                                                                |
| ----------------- | ------------------------------------------------------------------------------------------ |
| `Pauli`           | Enumeration for the Pauli matrices used in quantum computing.                              |
| `PauliTerm`       | A term in a Hamiltonian, represented as a product of single-qubit Pauli matrices.          |
| `IndexedPauli`    | A single-qubit Pauli matrix on a specific qubit given by its index.                        |
| `SparsePauliTerm` | A term in the Hamiltonian, represented as a sparse product of single-qubit Pauli matrices. |
| `SparsePauliOp`   | Represents a collection of sparse Pauli operators.                                         |

### Pauli

Enumeration for the Pauli matrices used in quantum computing.

Represents the four Pauli matrices used in quantum mechanics: Identity (I), X, Y, and Z operators.
The Pauli matrices are defined as:

$$
I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}
$$

$$
X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
$$

$$
Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}
$$

$$
Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}
$$

**Attributes:**

| Name    | Type | Description |
| ------- | ---- | ----------- |
| [I](#i) |      |             |
| [X](#x) |      |             |
| [Y](#y) |      |             |
| [Z](#z) |      |             |

### I

```python theme={null}
I = '0'
```

### X

```python theme={null}
X = '1'
```

### Y

```python theme={null}
Y = '2'
```

### Z

```python theme={null}
Z = '3'
```

### PauliTerm

A term in a Hamiltonian, represented as a product of single-qubit Pauli matrices.

**Attributes:**

| Name          | Type            | Description                                                                           |
| ------------- | --------------- | ------------------------------------------------------------------------------------- |
| `pauli`       | `CArray[Pauli]` | The list of the chosen Pauli operators in the term, corresponds to a product of them. |
| `coefficient` | `CReal`         | The coefficient of the term (floating number).                                        |

### pauli

`pauli: CArray[Pauli]`

### coefficient

`coefficient: CReal`

### IndexedPauli

A single-qubit Pauli matrix on a specific qubit given by its index.

**Attributes:**

| Name    | Type    | Description                               |
| ------- | ------- | ----------------------------------------- |
| `pauli` | `Pauli` | The Pauli operator.                       |
| `index` | `CInt`  | The index of the qubit being operated on. |

### pauli

`pauli: Pauli`

### index

`index: CInt`

### SparsePauliTerm

A term in the Hamiltonian, represented as a sparse product of single-qubit Pauli
matrices.

Attributes:
paulis (CArray\[IndexedPauli]): The list of chosen sparse Pauli operators in the term corresponds to a product of them. (See IndexedPauli)
coefficient (CReal): The coefficient of the term (floating number).

**Methods:**

| Name                       | Description |
| -------------------------- | ----------- |
| [cmp\_paulis](#cmp_paulis) |             |

### paulis

`paulis: CArray[IndexedPauli]`

### coefficient

`coefficient: CReal`

### SparsePauliOp

Represents a collection of sparse Pauli operators.

**Methods:**

| Name                                                      | Description |
| --------------------------------------------------------- | ----------- |
| [get\_tuples\_representation](#get_tuples_representation) |             |

**Attributes:**

| Name         | Type                      | Description                                                                                     |
| ------------ | ------------------------- | ----------------------------------------------------------------------------------------------- |
| `terms`      | `CArray[SparsePauliTerm]` | The list of chosen sparse Pauli terms, corresponds to a product of them. (See: SparsePauliTerm) |
| `num_qubits` | `CInt`                    | The number of qubits in the Hamiltonian.                                                        |

### terms

`terms: list[SparsePauliTerm]`

### num\_qubits

`num_qubits: int`
options:
show\_source: false
show\_if\_no\_docstring: false

options:
show\_source: false
show\_if\_no\_docstring: false
Members:

| Name            | Description                                                   |
| --------------- | ------------------------------------------------------------- |
| `SparsePauliOp` | Represents a collection of sparse Pauli operators.            |
| `Pauli`         | Enumeration for the Pauli matrices used in quantum computing. |

### SparsePauliOp

Represents a collection of sparse Pauli operators.

**Methods:**

| Name                                                      | Description |
| --------------------------------------------------------- | ----------- |
| [get\_tuples\_representation](#get_tuples_representation) |             |

**Attributes:**

| Name         | Type                      | Description                                                                                     |
| ------------ | ------------------------- | ----------------------------------------------------------------------------------------------- |
| `terms`      | `CArray[SparsePauliTerm]` | The list of chosen sparse Pauli terms, corresponds to a product of them. (See: SparsePauliTerm) |
| `num_qubits` | `CInt`                    | The number of qubits in the Hamiltonian.                                                        |

### terms

`terms: list[SparsePauliTerm]`

### num\_qubits

`num_qubits: int`

### Pauli

Enumeration for the Pauli matrices used in quantum computing.

Represents the four Pauli matrices used in quantum mechanics: Identity (I), X, Y, and Z operators.
The Pauli matrices are defined as:

$$
I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}
$$

$$
X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
$$

$$
Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}
$$

$$
Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}
$$

**Attributes:**

| Name    | Type | Description |
| ------- | ---- | ----------- |
| [I](#i) |      |             |
| [X](#x) |      |             |
| [Y](#y) |      |             |
| [Z](#z) |      |             |

### I

```python theme={null}
I = '0'
```

### X

```python theme={null}
X = '1'
```

### Y

```python theme={null}
Y = '2'
```

### Z

```python theme={null}
Z = '3'
```

options:
show\_source: false
show\_if\_no\_docstring: false