> ## 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.
# Partial Uniform State Preparations
Open this notebook in GitHub to run it yourself
The functions `prepare_uniform_trimmed_state` and `prepare_uniform_interval_state` create states with uniform superposition over a discrete interval of the possible states.
Both scale polynomially with the number of qubits.
## Uniform Trimmed State
Function: `prepare_uniform_trimmed_state`
Arguments:
* `m: CInt` - number of states to load.
* `q: QArray[QBit]` - quantum variable to load the state into.
The function loads the following superposition:
$$
|\psi\rangle = \frac{1}{\sqrt{m}}\sum_{i=0}^{m-1}{|i\rangle}
$$
#
## Example
Prepare the following state on a variable of size 4 qubits.:
$$
|\psi\rangle = \frac{1}{\sqrt{3}}\sum_{i=0}^{2}{|i\rangle}
$$
```python theme={null}
import matplotlib.pyplot as plt
from classiq import *
@qfunc
def main(x: Output[QNum]):
allocate(4, x)
prepare_uniform_trimmed_state(3, x)
qmod = create_model(main)
qprog = synthesize(qmod)
```
```python theme={null}
result = execute(qprog).result_value()
counts = result.parsed_counts
```
```python theme={null}
plt.figure(figsize=(4, 3))
plt.bar(
[c.state["x"] for c in counts],
[c.shots for c in counts],
color="skyblue",
edgecolor="black",
)
plt.xlabel("state")
plt.ylabel("shots")
```
**Output:**
```
Text(0, 0.5, 'shots')
```
## Uniform Interval State
Function: `prepare_uniform_interval_state`
Arguments:
* `start: CInt` - first state to be loaded.
* `end: CInt` - boundary of the loaded states (not including).
* `q: QArray[QBit]` - quantum variable to load the state into.
The function loads the following superposition:
$$
|\psi\rangle = \frac{1}{\sqrt{end-start}}\sum_{i=start}^{end-1}{|i\rangle}
$$
#
## Example
Prepare the following state on a variable of size 5 qubits.:
$$
|\psi\rangle = \frac{1}{\sqrt{6}}\sum_{i=2}^{7}{|i\rangle}
$$
```python theme={null}
@qfunc
def main(x: Output[QNum]):
allocate(5, x)
prepare_uniform_interval_state(2, 8, x)
qmod = create_model(main)
qprog = synthesize(qmod)
```
```python theme={null}
result = execute(qprog).result_value()
counts = result.parsed_counts
```
```python theme={null}
plt.figure(figsize=(5, 3))
plt.bar(
[c.state["x"] for c in counts],
[c.shots for c in counts],
color="skyblue",
edgecolor="black",
)
plt.xlabel("state")
plt.ylabel("shots")
```
**Output:**
```
Text(0, 0.5, 'shots')
```
