# LinearPauliRotations

*class *`qiskit.circuit.library.LinearPauliRotations(num_state_qubits=None, slope=1, offset=0, basis='Y', name='LinRot')`

Bases: `FunctionalPauliRotations`

Linearly-controlled X, Y or Z rotation.

For a register of state qubits $|x\rangle$, a target qubit $|0\rangle$ and the basis `'Y'`

this circuit acts as:

```
q_0: ─────────────────────────■───────── ... ──────────────────────
│
.
│
q_(n-1): ─────────────────────────┼───────── ... ───────────■──────────
┌────────────┐ ┌───────┴───────┐ ┌─────────┴─────────┐
q_n: ─┤ RY(offset) ├──┤ RY(2^0 slope) ├ ... ┤ RY(2^(n-1) slope) ├
└────────────┘ └───────────────┘ └───────────────────┘
```

This can for example be used to approximate linear functions, with $a =$ `slope`

$/2$ and $b =$ `offset`

$/2$ and the basis `'Y'`

:

Since for small arguments $\sin(x) \approx x$ this operator can be used to approximate linear functions.

Create a new linear rotation circuit.

**Parameters**

**num_state_qubits**(*int**| None*) – The number of qubits representing the state $|x\rangle$.**slope**(*float*) – The slope of the controlled rotation.**offset**(*float*) – The offset of the controlled rotation.**basis**(*str*) – The type of Pauli rotation (‘X’, ‘Y’, ‘Z’).**name**(*str*) – The name of the circuit object.

## Attributes

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

### basis

The kind of Pauli rotation to be used.

Set the basis to ‘X’, ‘Y’ or ‘Z’ for controlled-X, -Y, or -Z rotations respectively.

**Returns**

The kind of Pauli rotation used in controlled rotation.

### calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`

### clbits

Returns a list of classical bits in the order that the registers were added.

### data

### extension_lib

Default value: `'include "qelib1.inc";'`

### global_phase

Return the global phase of the current circuit scope in radians.

### header

Default value: `'OPENQASM 2.0;'`

### instances

Default value: `163`

### layout

Return any associated layout information about the circuit

This attribute contains an optional `TranspileLayout`

object. This is typically set on the output from `transpile()`

or `PassManager.run()`

to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the `transpile()`

function, an initial layout which permutes the qubits based on the selected physical qubits on the `Target`

, and a final layout which is an output permutation caused by `SwapGate`

s inserted during routing.

### metadata

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided `dict`

of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

### num_ancilla_qubits

The minimum number of ancilla qubits in the circuit.

**Returns**

The minimal number of ancillas required.

### num_ancillas

Return the number of ancilla qubits.

### num_clbits

Return number of classical bits.

### num_parameters

### num_qubits

Return number of qubits.

### num_state_qubits

The number of state qubits representing the state $|x\rangle$.

**Returns**

The number of state qubits.

### offset

The angle of the single qubit offset rotation on the target qubit.

Before applying the controlled rotations, a single rotation of angle `offset`

is applied to the target qubit.

**Returns**

The offset angle.

### op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

**Returns**

List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`

.

**Raises**

**AttributeError** – When circuit is not scheduled.

### parameters

### prefix

Default value: `'circuit'`

### qregs

Type: `list[QuantumRegister]`

A list of the quantum registers associated with the circuit.

### qubits

Returns a list of quantum bits in the order that the registers were added.

### slope

The multiplicative factor in the rotation angle of the controlled rotations.

The rotation angles are `slope * 2^0`

, `slope * 2^1`

, … , `slope * 2^(n-1)`

where `n`

is the number of state qubits.

**Returns**

The rotation angle common in all controlled rotations.