> ## Documentation Index
> Fetch the complete documentation index at: https://docs.haiqu.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# Distribution Loading

#### Haiqu.distribution\_loading(num\_qubits, distribution\_name, interval\_start, interval\_end, loc=0, scale=1, num\_layers=1, truncation\_cutoff=1e-06, name=None, \*\*shape)

Generate a quantum circuit that prepares a probability distribution.

Given the description of a probability distribution function (PDF), this method creates a Data Loading job that runs in
the Haiqu cloud. The result of this job is a circuit which can be used to supply the PDF to a quantum algorithm for
processing. The cost and time of this job can be estimated with [`distribution_loading_estimates()`](../index.md#haiqu.sdk.quantum_haiqu.Haiqu.distribution_loading_estimates).

The complexity of the generated circuit can be controlled by the `num_layers` and `truncation_cutoff` parameters.

* **Parameters:**
  * **num\_qubits** (*int*) -- The number of qubits in the generated circuit (from 1 to 1000 qubits).
  * **distribution\_name** (*str*) -- The name of the distribution. Can be any of the continuous distributions in `scipy.stats`.
  * **interval\_start** (*Real*) -- The beginning of the interval.
  * **interval\_end** (*Real*) -- The end of the interval.
  * **loc** (*Real*) -- The location to which to shift the distribution. Defaults to 0.
  * **scale** (*Real*) -- The scaling factor by which to stretch the distribution. Defaults to 1.
  * **num\_layers** (*int*) -- The number of layers in the generated circuit (from 1 to 15 layers).
    More layers can improve the quality of the output
    distribution at the cost of a deeper circuit. Defaults to 1.
  * **truncation\_cutoff** (*Real*) -- The entanglement cutoff for later layers. Increasing this threshold may result in a smaller
    (but more approximate) circuit. Defaults to `1e-6`.
  * **name** (*str* *|* *None*) -- The name for the job and the produced circuit. If `None` (default), a name will be automatically
    generated.
  * **\*\*shape** -- Additional distribution parameters, required by some distributions. Refer to the distribution documentation
    in `scipy.stats` for more details.
* **Returns:**
  The Data Loading job that will generate the circuit for the probability distribution.
  : Call `job.result()` to retrieve a Qiskit-compatible gate (`HaiquCircuitGate`) that prepares the requested
  probability distribution on `num_qubits` qubits. `job.quality` is the achieved state fidelity vs. the ideal
  target distribution; `job.info` exposes loader metadata (`fidelity`).
  Run `help(job.result)` for the full description of result and `info` contents.
* **Return type:**
  DataLoadingJobModel

#### Examples

```python theme={null}
>>> num_qubits = 4
>>> job = haiqu.distribution_loading(
...     num_qubits=num_qubits,
...     distribution_name="norm",
...     interval_start=-3,
...     interval_end=3,
...     name=f"Normal distribution ({num_qubits} qubits)",
... )
>>> dl_gate = job.result()  # dl_gate is a Qiskit-compatible gate
>>> fidelity = job.quality
>>> print(f"Normal distribution was loaded with fidelity {fidelity:.6f}")
Normal distribution was loaded with fidelity 0.999484
>>> circuit = qiskit.QuantumCircuit(num_qubits)
>>> circuit.append(dl_gate, range(num_qubits))
>>> circuit.draw()
     ┌────────────────────────────────────────────────────────────┐
q_0: ┤0                                                           ├
     │                                                            │
q_1: ┤1                                                           ├
     │  Haiqucircuit(circ-12345678-1234-5678-1234-567812345678,4) │
q_2: ┤2                                                           ├
     │                                                            │
q_3: ┤3                                                           ├
     └────────────────────────────────────────────────────────────┘
```

#### Haiqu.distribution\_loading\_estimates(num\_qubits, distribution\_name, interval\_start, interval\_end, loc=0, scale=1, num\_layers=1, truncation\_cutoff=1e-06, name=None, \*\*shape)

Estimate the cost and time of a Data Loading job created by [`distribution_loading()`](../index.md#haiqu.sdk.quantum_haiqu.Haiqu.distribution_loading).

The parameters are the same as for [`distribution_loading()`](../index.md#haiqu.sdk.quantum_haiqu.Haiqu.distribution_loading). Once you discover values that result in acceptable cost
and time estimates, you can remove `_estimates` from the end of the method name and call [`distribution_loading()`](../index.md#haiqu.sdk.quantum_haiqu.Haiqu.distribution_loading).

* **Parameters:**
  * **num\_qubits** (*int*) -- The number of qubits in the generated circuit (from 1 to 1000 qubits).
  * **distribution\_name** (*str*) -- The name of the distribution. Can be any of the continuous distributions in `scipy.stats`.
  * **interval\_start** (*Real*) -- The beginning of the interval.
  * **interval\_end** (*Real*) -- The end of the interval.
  * **loc** (*Real*) -- The location to which to shift the distribution. Defaults to 0.
  * **scale** (*Real*) -- The scaling factor by which to stretch the distribution. Defaults to 1.
  * **num\_layers** (*int*) -- The number of layers in the generated circuit (from 1 to 15 layers).
    More layers can improve the quality of the output
    distribution at the cost of a deeper circuit. Defaults to 1.
  * **truncation\_cutoff** (*Real*) -- The entanglement cutoff for later layers. Increasing this threshold may result in a smaller
    (but more approximate) circuit. Defaults to `1e-6`.
  * **name** (*str* *|* *None*) -- The name for the job and the produced circuit. If `None` (default), a name will be automatically
    generated.
  * **\*\*shape** -- Additional distribution parameters, required by some distributions. Refer to the distribution documentation
    in `scipy.stats` for more details.
* **Returns:**
  The estimated time (in seconds) and cost (in Haiqu Credits).
* **Return type:**
  DataLoadingEstimatesModel

#### Examples

```python theme={null}
>>> est = haiqu.distribution_loading_estimates(
...     num_qubits=10,
...     distribution_name="norm",
...     interval_start=-3,
...     interval_end=3
>>> )
>>> est
DataLoadingEstimatesModel(estimated_time=0.22770169152050562, estimated_cost=0.010079648405964921)
>>> est.draw()  # in Jupyter notebook
```