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PolynomialPauliRotationsGate

class qiskit.circuit.library.PolynomialPauliRotationsGate(num_state_qubits, coeffs=None, basis='Y', label=None)

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Bases: Gate

A gate implementing polynomial Pauli rotations.

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

∣i⟩∣0⟩↦cos⁡(p(i)2)∣i⟩∣0⟩+sin⁡(p(i)2)∣i⟩∣1⟩|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=∑i=0n−12iqi,x = \sum_{i=0}^{n-1} 2^i q_i,

we can write

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

where cc are the input coefficients, coeffs.

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

Parameters

  • num_state_qubits (int) – The number of qubits representing the state.
  • coeffs (list[float] | None) – The coefficients of the polynomial. coeffs[i] is the coefficient of the i-th power of x. Defaults to linear: [0, 1].
  • basis (str) – The type of Pauli rotation (‘X’, ‘Y’, ‘Z’).
  • label (str | None) – A label for the gate.

Attributes

base_class

Get the base class of this instruction. This is guaranteed to be in the inheritance tree of self.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for _all_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioral perspective. In particular, you should not override base_class if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrized gate with a particular set of parameters for the purposes of distinguishing it in a Target from the full parametrized gate.

This is often exactly equivalent to type(obj), except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

>>> isinstance(XGate(), XGate)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that Instruction.name should be a more suitable discriminator in most situations.

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

label

Return instruction label

mutable

Is this instance is a mutable unique instance or not.

If this attribute is False the gate instance is a shared singleton and is not mutable.

name

Return the name.

num_clbits

Return the number of clbits.

num_qubits

Return the number of qubits.

params

The parameters of this Instruction. Ideally these will be gate angles.

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