---
title: BalancedUniformPauli (latest version)
description: API reference for samplomatic.distributions.BalancedUniformPauli in the latest version of samplomatic
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/samplomatic/auto/distributions-balanced-uniform-pauli
---

# BalancedUniformPauli

*class* `samplomatic.distributions.BalancedUniformPauli(num_subsystems: int)`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/distributions/balanced_uniform_pauli.py#L23-L53)

Bases: [`Distribution`](/docs/api/samplomatic/auto/distributions-distribution "samplomatic.distributions.distribution.Distribution")

The balanced uniform distribution over virtual Pauli gates.

Here, *balanced* means that on every qubit, each of the four Paulis appears the same number of times, provided that the requested number of samples is a multiple of four. Moreover, when the number of samples is a multiple of two, it is promised that, for each qubit, X or Y is sampled the same number of times as I or Z.

The sampling algorithm is simply to draw four times fewer n-qubit Paulis uniformly and iid than requested, and then replicate each four times with respective multiplications by $I^{\otimes}n$, $X^{\otimes}n$, $Z^{\otimes}n$, and $Y^{\otimes}n$, truncating the samples if their requested number is not a multiple of four. Randomizations are ordered such that the four replications are consecutive. The particular ordering of the four multiplicative terms— $I$ then $X$ then $Z$ then $Y$ —is what provides the guarantee that for each qubit, X or Y is sampled the same number of times as I or Z, even if the number of samples is even but not a multiple of four.

**Parameters**

**num\_subsystems** – The number of subsystems this distribution samples.

**Attributes Summary**

|                                                                                                                                                 |                                      |
| ----------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------ |
| [`register_type`](#samplomatic.distributions.BalancedUniformPauli.register_type "samplomatic.distributions.BalancedUniformPauli.register_type") | The virtual gate type being sampled. |

**Methods Summary**

|                                                                                                                                       |                          |
| ------------------------------------------------------------------------------------------------------------------------------------- | ------------------------ |
| [`sample`](#samplomatic.distributions.BalancedUniformPauli.sample "samplomatic.distributions.BalancedUniformPauli.sample")(size, rng) | Sample the distribution. |

**Attributes Documentation**

### register\_type

**Methods Documentation**

### sample

`sample(size, rng)`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/distributions/balanced_uniform_pauli.py#L48-L53)

Sample the distribution.

**Parameters**

- **size** – The number elements to sample.
- **rng** – A randomness generator.

**Returns**

The samples.