PiecewisePolynomialPauliRotations
class PiecewisePolynomialPauliRotations(num_state_qubits=None, breakpoints=None, coeffs=None, basis='Y', name='pw_poly')
Bases: qiskit.circuit.library.arithmetic.functional_pauli_rotations.FunctionalPauliRotations
Piecewise-polynomially-controlled Pauli rotations.
This class implements a piecewise polynomial (not necessarily continuous) function, , on qubit amplitudes, which is defined through breakpoints and coefficients as follows. Suppose the breakpoints are a subset of , where is the number of state qubits. Further on, denote the corresponding coefficients by , where is the highest degree among all polynomials.
Then is defined as:
where if given the same number of breakpoints as polynomials, we implicitly assume .
Note the factor in the coefficients of , this is consistent with Qiskit’s Pauli rotations.
Examples
>>> from qiskit import QuantumCircuit
>>> from qiskit.circuit.library.arithmetic.piecewise_polynomial_pauli_rotations import\
... PiecewisePolynomialPauliRotations
>>> qubits, breakpoints, coeffs = (2, [0, 2], [[0, -1.2],[-1, 1, 3]])
>>> poly_r = PiecewisePolynomialPauliRotations(num_state_qubits=qubits,
...breakpoints=breakpoints, coeffs=coeffs)
>>>
>>> qc = QuantumCircuit(poly_r.num_qubits)
>>> qc.h(list(range(qubits)));
>>> qc.append(poly_r.to_instruction(), list(range(qc.num_qubits)));
>>> qc.draw()
┌───┐┌──────────┐
q_0: ┤ H ├┤0 ├
├───┤│ │
q_1: ┤ H ├┤1 ├
└───┘│ │
q_2: ─────┤2 ├
│ pw_poly │
q_3: ─────┤3 ├
│ │
q_4: ─────┤4 ├
│ │
q_5: ─────┤5 ├
└──────────┘References
[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).
Optimizing Quantum Circuits for Arithmetic. arXiv:1805.12445
[2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2022).
Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation. ACM Transactions on Quantum Computing 3, 1, Article 2
Parameters
- num_state_qubits (
Optional[int]) – The number of qubits representing the state. - breakpoints (
Optional[List[int]]) – The breakpoints to define the piecewise-linear function. Defaults to[0]. - coeffs (
Optional[List[List[float]]]) – The coefficients of the polynomials for different segments of the - x (piecewise-linear function. coeffs[j][i] is the coefficient of the i-th power of) –
- polynomial. (for the j-th) – Defaults to linear:
[[1]]. - basis (
str) – The type of Pauli rotation ('X','Y','Z'). - name (
str) – The name of the circuit.
Methods Defined Here
evaluate
PiecewisePolynomialPauliRotations.evaluate(x)
Classically evaluate the piecewise polynomial rotation.
Parameters
x (float) – Value to be evaluated at.
Return type
float
Returns
Value of piecewise polynomial function at x.
Attributes
ancillas
Returns a list of ancilla bits in the order that the registers were added.
Return type
List[AncillaQubit]
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.
Return type
str
Returns
The kind of Pauli rotation used in controlled rotation.
breakpoints
The breakpoints of the piecewise polynomial function.
The function is polynomial in the intervals [point_i, point_{i+1}] where the last point implicitly is 2**(num_state_qubits + 1).
Return type
List[int]
Returns
The list of breakpoints.
calibrations
Return calibration dictionary.
The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}
Return type
dict
clbits
coeffs
The coefficients of the polynomials.
Return type
List[List[float]]
Returns
The polynomial coefficients per interval as nested lists.
contains_zero_breakpoint
Whether 0 is the first breakpoint.
Return type
bool
Returns
True, if 0 is the first breakpoint, otherwise False.
data
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 2502
mapped_coeffs
The coefficients mapped to the internal representation, since we only compare x>=breakpoint.
Return type
List[List[float]]
Returns
The mapped coefficients.
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.
Return type
dict
num_ancilla_qubits
The minimum number of ancilla qubits in the circuit.
Return type
int
Returns
The minimal number of ancillas required.
num_ancillas
Return the number of ancilla qubits.
Return type
int
num_clbits
Return number of classical bits.
Return type
int
num_parameters
Return type
int
num_qubits
Return number of qubits.
Return type
int
num_state_qubits
The number of state qubits representing the state .
Return type
int
Returns
The number of state qubits.
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.
Return type
List[int]
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
Return type
ParameterView
prefix
Default value: 'circuit'
qregs
A list of the quantum registers associated with the circuit.