363 lines
11 KiB
Plaintext
363 lines
11 KiB
Plaintext
---
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title: PiecewisePolynomialPauliRotations
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description: API reference for qiskit.circuit.library.PiecewisePolynomialPauliRotations
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.PiecewisePolynomialPauliRotations
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---
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# PiecewisePolynomialPauliRotations
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<Class id="qiskit.circuit.library.PiecewisePolynomialPauliRotations" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.23/qiskit/circuit/library/arithmetic/piecewise_polynomial_pauli_rotations.py" signature="PiecewisePolynomialPauliRotations(num_state_qubits=None, breakpoints=None, coeffs=None, basis='Y', name='pw_poly')" modifiers="class">
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Bases: [`qiskit.circuit.library.arithmetic.functional_pauli_rotations.FunctionalPauliRotations`](qiskit.circuit.library.FunctionalPauliRotations "qiskit.circuit.library.arithmetic.functional_pauli_rotations.FunctionalPauliRotations")
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Piecewise-polynomially-controlled Pauli rotations.
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This class implements a piecewise polynomial (not necessarily continuous) function, $f(x)$, on qubit amplitudes, which is defined through breakpoints and coefficients as follows. Suppose the breakpoints $(x_0, ..., x_J)$ are a subset of $[0, 2^n-1]$, where $n$ is the number of state qubits. Further on, denote the corresponding coefficients by $[a_{j,1},...,a_{j,d}]$, where $d$ is the highest degree among all polynomials.
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Then $f(x)$ is defined as:
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$$
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\begin{split}f(x) = \begin{cases}
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0, x < x_0 \\
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\sum_{i=0}^{i=d}a_{j,i}/2 x^i, x_j \leq x < x_{j+1}
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\end{cases}\end{split}
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$$
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where if given the same number of breakpoints as polynomials, we implicitly assume $x_{J+1} = 2^n$.
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<Admonition title="Note" type="note">
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Note the $1/2$ factor in the coefficients of $f(x)$, this is consistent with Qiskit’s Pauli rotations.
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</Admonition>
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**Examples**
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```python
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>>> from qiskit import QuantumCircuit
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>>> from qiskit.circuit.library.arithmetic.piecewise_polynomial_pauli_rotations import\
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... PiecewisePolynomialPauliRotations
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>>> qubits, breakpoints, coeffs = (2, [0, 2], [[0, -1.2],[-1, 1, 3]])
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>>> poly_r = PiecewisePolynomialPauliRotations(num_state_qubits=qubits,
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...breakpoints=breakpoints, coeffs=coeffs)
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>>>
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>>> qc = QuantumCircuit(poly_r.num_qubits)
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>>> qc.h(list(range(qubits)));
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>>> qc.append(poly_r.to_instruction(), list(range(qc.num_qubits)));
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>>> qc.draw()
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┌───┐┌──────────┐
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q_0: ┤ H ├┤0 ├
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├───┤│ │
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q_1: ┤ H ├┤1 ├
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└───┘│ │
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q_2: ─────┤2 ├
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│ pw_poly │
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q_3: ─────┤3 ├
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│ │
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q_4: ─────┤4 ├
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│ │
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q_5: ─────┤5 ├
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└──────────┘
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```
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**References**
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**\[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).**
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Optimizing Quantum Circuits for Arithmetic. [arXiv:1805.12445](http://arxiv.org/abs/1805.12445)
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**\[2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2022).**
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Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation. [ACM Transactions on Quantum Computing 3, 1, Article 2](https://doi.org/10.1145/3490631)
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**Parameters**
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* **num\_state\_qubits** (`Optional`\[`int`]) – The number of qubits representing the state.
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* **breakpoints** (`Optional`\[`List`\[`int`]]) – The breakpoints to define the piecewise-linear function. Defaults to `[0]`.
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* **coeffs** (`Optional`\[`List`\[`List`\[`float`]]]) – The coefficients of the polynomials for different segments of the
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* **x** (*piecewise-linear function. coeffs\[j]\[i] is the coefficient of the i-th power of*) –
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* **polynomial.** (*for the j-th*) – Defaults to linear: `[[1]]`.
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* **basis** (`str`) – The type of Pauli rotation (`'X'`, `'Y'`, `'Z'`).
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* **name** (`str`) – The name of the circuit.
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## Methods Defined Here
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### evaluate
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<Function id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.evaluate" signature="PiecewisePolynomialPauliRotations.evaluate(x)">
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Classically evaluate the piecewise polynomial rotation.
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**Parameters**
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**x** (`float`) – Value to be evaluated at.
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**Return type**
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`float`
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**Returns**
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Value of piecewise polynomial function at x.
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</Function>
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.ancillas">
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Returns a list of ancilla bits in the order that the registers were added.
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**Return type**
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`List`\[[`AncillaQubit`](qiskit.circuit.AncillaQubit "qiskit.circuit.quantumregister.AncillaQubit")]
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</Attribute>
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### basis
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.basis">
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The kind of Pauli rotation to be used.
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Set the basis to ‘X’, ‘Y’ or ‘Z’ for controlled-X, -Y, or -Z rotations respectively.
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**Return type**
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`str`
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**Returns**
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The kind of Pauli rotation used in controlled rotation.
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</Attribute>
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### breakpoints
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.breakpoints">
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The breakpoints of the piecewise polynomial function.
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The function is polynomial in the intervals `[point_i, point_{i+1}]` where the last point implicitly is `2**(num_state_qubits + 1)`.
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**Return type**
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`List`\[`int`]
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**Returns**
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The list of breakpoints.
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.calibrations">
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Return calibration dictionary.
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The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`
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**Return type**
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`dict`
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.clbits">
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Returns a list of classical bits in the order that the registers were added.
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**Return type**
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`List`\[[`Clbit`](qiskit.circuit.Clbit "qiskit.circuit.classicalregister.Clbit")]
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</Attribute>
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### coeffs
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.coeffs">
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The coefficients of the polynomials.
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**Return type**
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`List`\[`List`\[`float`]]
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**Returns**
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The polynomial coefficients per interval as nested lists.
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</Attribute>
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### contains\_zero\_breakpoint
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.contains_zero_breakpoint">
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Whether 0 is the first breakpoint.
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**Return type**
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`bool`
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**Returns**
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True, if 0 is the first breakpoint, otherwise False.
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</Attribute>
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### data
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.data" />
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### extension\_lib
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.extension_lib" attributeValue="'include "qelib1.inc";'" />
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### global\_phase
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.global_phase">
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Return the global phase of the circuit in radians.
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**Return type**
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`Union`\[[`ParameterExpression`](qiskit.circuit.ParameterExpression "qiskit.circuit.parameterexpression.ParameterExpression"), `float`]
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</Attribute>
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### header
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.header" attributeValue="'OPENQASM 2.0;'" />
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### instances
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.instances" attributeValue="2245" />
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### mapped\_coeffs
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.mapped_coeffs">
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The coefficients mapped to the internal representation, since we only compare x>=breakpoint.
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**Return type**
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`List`\[`List`\[`float`]]
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**Returns**
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The mapped coefficients.
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</Attribute>
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### metadata
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.metadata">
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The user provided metadata associated with the circuit
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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.
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**Return type**
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`dict`
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</Attribute>
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### num\_ancilla\_qubits
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.num_ancilla_qubits">
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The minimum number of ancilla qubits in the circuit.
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**Return type**
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`int`
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**Returns**
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The minimal number of ancillas required.
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</Attribute>
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### num\_ancillas
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.num_ancillas">
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Return the number of ancilla qubits.
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**Return type**
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`int`
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.num_clbits">
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Return number of classical bits.
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**Return type**
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`int`
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.num_parameters">
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**Return type**
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`int`
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.num_qubits">
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Return number of qubits.
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**Return type**
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`int`
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</Attribute>
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### num\_state\_qubits
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.num_state_qubits">
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The number of state qubits representing the state $|x\rangle$.
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**Return type**
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`int`
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**Returns**
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The number of state qubits.
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</Attribute>
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### op\_start\_times
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.op_start_times">
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Return a list of operation start times.
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This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.
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**Return type**
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`List`\[`int`]
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**Returns**
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List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.
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**Raises**
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**AttributeError** – When circuit is not scheduled.
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</Attribute>
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### parameters
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.parameters">
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**Return type**
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`ParameterView`
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.prefix" attributeValue="'circuit'" />
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### qregs
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.qregs">
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A list of the quantum registers associated with the circuit.
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</Attribute>
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### qubits
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<Attribute id="qiskit.circuit.library.PiecewisePolynomialPauliRotations.qubits">
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Returns a list of quantum bits in the order that the registers were added.
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**Return type**
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`List`\[[`Qubit`](qiskit.circuit.Qubit "qiskit.circuit.quantumregister.Qubit")]
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</Attribute>
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</Class>
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