# 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

A list of `AncillaQubit`

s in the order that they were added. You should not mutate this.

### 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

A list of `Clbit`

s in the order that they were added. You should not mutate this.

### data

### global_phase

The global phase of the current circuit scope in radians.

### instances

Default value: `178`

### 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

Arbitrary user-defined metadata for the circuit.

Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.

### 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_captured_vars

The number of real-time classical variables in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_vars()`

iterable. If this is non-zero, `num_input_vars`

must be zero.

### num_clbits

Return number of classical bits.

### num_declared_vars

The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.

This is the length of the `iter_declared_vars()`

iterable.

### num_input_vars

The number of real-time classical variables in the circuit marked as circuit inputs.

This is the length of the `iter_input_vars()`

iterable. If this is non-zero, `num_captured_vars`

must be zero.

### 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.

### num_vars

The number of real-time classical variables in the circuit.

This is the length of the `iter_vars()`

iterable.

### 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 `QuantumRegister`

s in this circuit. You should not mutate this.

### qubits

A list of `Qubit`

s in the order that they were added. You should not mutate this.

### 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.

### name

Type: `str`

A human-readable name for the circuit.

### cregs

Type: `list[ClassicalRegister]`

A list of the `ClassicalRegister`

s in this circuit. You should not mutate this.

### duration

Type: `int | float | None`

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by `unit`

.

### unit

The unit that `duration`

is specified in.