# PolynomialPauliRotations

class qiskit.circuit.library.PolynomialPauliRotations(num_state_qubits=None, coeffs=None, basis='Y', name='poly')

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A circuit implementing polynomial Pauli rotations.

For a polynomial $p(x)$, a basis state $|i\rangle$ and a target qubit $|0\rangle$ this operator acts as:

$|i\rangle |0\rangle \mapsto \cos\left(\frac{p(i)}{2}\right) |i\rangle |0\rangle + \sin\left(\frac{p(i)}{2}\right) |i\rangle |1\rangle$

Let n be the number of qubits representing the state, d the degree of p(x) and q_i the qubits, where q_0 is the least significant qubit. Then for

$x = \sum_{i=0}^{n-1} 2^i q_i,$

we can write

$p(x) = \sum_{j=0}^{j=d} c_j x^j$

where $c$ are the input coefficients, coeffs.

Prepare an approximation to a state with amplitudes specified by a polynomial.

Parameters

## Attributes

### ancillas

A list of AncillaQubits 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 Clbits in the order that they were added. You should not mutate this.

### coeffs

The coefficients of the polynomial.

coeffs[i] is the coefficient of the i-th power of the function input $x$, that means that the rotation angles are based on the coefficients value, following the formula

$c_j x^j , j=0, ..., d$

where $d$ is the degree of the polynomial $p(x)$ and $c$ are the coefficients coeffs.

Returns

The coefficients of the polynomial.

### degree

Return the degree of the polynomial, equals to the number of coefficients minus 1.

Returns

The degree of the polynomial. If the coefficients have not been set, return 0.

### global_phase

The global phase of the current circuit scope in radians.

### instances

Default value: 259

### 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 SwapGates inserted during routing.

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_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.

### 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(opens in a new tab) – When circuit is not scheduled.

### prefix

Default value: 'circuit'

### qregs

Type: list[QuantumRegister]

A list of the QuantumRegisters in this circuit. You should not mutate this.

### qubits

A list of Qubits in the order that they were added. You should not mutate this.

### name

Type: str

A human-readable name for the circuit.

### cregs

Type: list[ClassicalRegister]

A list of the ClassicalRegisters 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.