> ## 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.

# Utility Functions

Functions:

| Name                 | Description                       |
| -------------------- | --------------------------------- |
| `apply_to_all`       | \[Qmod Classiq-library function]. |
| `hadamard_transform` | \[Qmod Classiq-library function]. |
| `modular_increment`  | \[Qmod Classiq-library function]. |

### apply\_to\_all

<pre><code>apply\_to\_all(
gate\_operand: QCallable\[Annotated\[QBit, target]],
target: QArray\[QBit]
) -> None</code></pre>

\[Qmod Classiq-library function]

Applies the single-qubit operand `gate_operand` to each qubit in the qubit
array `target`.

**Parameters:**

| Name           | Type                                 | Description                                                | Default    |
| -------------- | ------------------------------------ | ---------------------------------------------------------- | ---------- |
| `gate_operand` | `QCallable[Annotated[QBit, target]]` | The single-qubit gate to apply to each qubit in the array. | *required* |
| `target`       | `QArray[QBit]`                       | The qubit array to apply the gate to.                      | *required* |

### hadamard\_transform

<pre><code>hadamard\_transform(
target: QArray\[QBit]
) -> None</code></pre>

\[Qmod Classiq-library function]

Applies Hadamard transform to the target qubits.

Corresponds to the braket notation:

$$
 H^{\otimes n} |x\rangle = \frac{1}{\sqrt{2^n}} \sum_{y=0}^{2^n - 1} (-1)^{x \\cdot y} |y\rangle
$$

**Parameters:**

| Name     | Type           | Description                               | Default    |
| -------- | -------------- | ----------------------------------------- | ---------- |
| `target` | `QArray[QBit]` | qubits to apply to Hadamard transform to. | *required* |

### modular\_increment

<pre><code>modular\_increment(
a: CInt,
x: QNum
) -> None</code></pre>

\[Qmod Classiq-library function]

Adds $a$ to $x$ modulo the range of $x$, assumed that $x$ is a non-negative integer and $a$ is an integer.
Mathematically it is described as:

$$
    x = (x+a)\ \mod \ 2^{x.size}-1
$$

**Parameters:**

| Name | Type   | Description                                                  | Default    |
| ---- | ------ | ------------------------------------------------------------ | ---------- |
| `a`  | `CInt` | A classical integer to be added to x.                        | *required* |
| `x`  | `QNum` | A quantum number that is assumed to be non-negative integer. | *required* |