PiecewisePolynomialPauliRotations
class qiskit.circuit.library.PiecewisePolynomialPauliRotations(num_state_qubits=None, breakpoints=None, coeffs=None, basis='Y', name='pw_poly')
Bases: 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.
Attributes
ancillas
Returns a list of ancilla bits in the order that the registers were added.
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.
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).
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}}
clbits
Returns a list of classical bits in the order that the registers were added.
coeffs
The coefficients of the polynomials.
Returns
The polynomial coefficients per interval as nested lists.
contains_zero_breakpoint
Whether 0 is the first breakpoint.
Returns
True, if 0 is the first breakpoint, otherwise False.
data
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
Return the global phase of the circuit in radians.
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 321
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.
mapped_coeffs
The coefficients mapped to the internal representation, since we only compare x>=breakpoint.
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.
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_clbits
Return number of classical bits.
num_parameters
num_qubits
Return number of qubits.
num_state_qubits
The number of state qubits representing the state .
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.
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 quantum registers associated with the circuit.
qubits
Returns a list of quantum bits in the order that the registers were added.
Methods
evaluate
evaluate(x)
Classically evaluate the piecewise polynomial rotation.
Parameters
x (float) – Value to be evaluated at.
Returns
Value of piecewise polynomial function at x.
Return type