---
title: QPDBasis (latest version)
description: API reference for qiskit_addon_cutting.qpd.QPDBasis in the latest version of qiskit-addon-cutting
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit-addon-cutting/qpd-qpd-basis
---

# QPDBasis

*class* `QPDBasis(maps, coeffs)`

[GitHub](https://github.com/Qiskit/qiskit-addon-cutting/tree/stable/0.10/qiskit_addon_cutting/qpd/qpd_basis.py)

Bases: [`object`](https://docs.python.org/3/library/functions.html#object)

Basis in which to decompose an operation.

This class defines a basis in which a quantum operation will be decomposed. The ideal (noise-free) quantum operation will be decomposed into a quasiprobabilistic mixture of noisy circuits.

Assign member variables.

**Parameters**

- **maps** ([`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)\[[`tuple`](https://docs.python.org/3/library/stdtypes.html#tuple)\[[`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)\[[`Instruction`](/docs/api/qiskit/qiskit.circuit.Instruction)], [`...`](https://docs.python.org/3/library/constants.html#Ellipsis)]]) – A sequence of tuples describing the noisy operations probabilistically used to simulate an ideal quantum operation.
- **coeffs** ([`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)\[[`float`](https://docs.python.org/3/library/functions.html#float)]) – Coefficients for quasiprobability representation. Each coefficient can be any real number.

**Returns**

None

## Attributes

### coeffs

Quasiprobability decomposition coefficients.

### kappa

Get the square root of the sampling overhead.

This quantity is the sum of the magnitude of the coefficients.

### maps

Get mappings for each qubit in the decomposition.

### num\_qubits

Get number of qubits that this decomposition acts on.

### overhead

Get the sampling overhead.

The sampling overhead is the square of the sum of the magnitude of the coefficients.

### probabilities

Get the probabilities on which the maps will be sampled.

## Methods

### from\_instruction

*static* `from_instruction(gate, /)`

Generate a [`QPDBasis`](#qiskit_addon_cutting.qpd.QPDBasis "qiskit_addon_cutting.qpd.QPDBasis") object, given a supported operation.

This static method is provided for convenience; it simply calls `qpdbasis_from_instruction()` under the hood.

**Parameters**

**gate** ([`Instruction`](/docs/api/qiskit/qiskit.circuit.Instruction)) – The instruction from which to instantiate a decomposition

**Return type**

[`QPDBasis`](#qiskit_addon_cutting.qpd.QPDBasis "qiskit_addon_cutting.qpd.qpd_basis.QPDBasis")

**Returns**

The newly-instantiated [`QPDBasis`](#qiskit_addon_cutting.qpd.QPDBasis "qiskit_addon_cutting.qpd.QPDBasis") object