PiecewiseChebyshev
class qiskit.circuit.library.PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')
Bases: BlueprintCircuit
Piecewise Chebyshev approximation to an input function.
For a given function and degree , this class implements a piecewise polynomial Chebyshev approximation on qubits to on the given intervals. All the polynomials in the approximation are of degree .
The values of the parameters are calculated according to [1] and see [2] for a more detailed explanation of the circuit construction and how it acts on the qubits.
Examples
import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit.library.arithmetic.piecewise_chebyshev import PiecewiseChebyshev
f_x, degree, breakpoints, num_state_qubits = lambda x: np.arcsin(1 / x), 2, [2, 4], 2
pw_approximation = PiecewiseChebyshev(f_x, degree, breakpoints, num_state_qubits)
pw_approximation._build()
qc = QuantumCircuit(pw_approximation.num_qubits)
qc.h(list(range(num_state_qubits)))
qc.append(pw_approximation.to_instruction(), qc.qubits)
qc.draw(output='mpl')
References
[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).
Optimizing Quantum Circuits for Arithmetic. arXiv:1805.12445
[2]: Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022).
Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. ACM Transactions on Quantum Computing 3, 1, Article 2
Parameters
- f_x (float | Callable[[int], float]) – the function to be approximated. Constant functions should be specified as f_x = constant.
- degree (int | None) – the degree of the polynomials. Defaults to
1. - breakpoints (list[int] | None) – the breakpoints to define the piecewise-linear function. Defaults to the full interval.
- num_state_qubits (int | None) – number of qubits representing the state.
- name (str) – The name of the circuit object.
Attributes
ancillas
A list of AncillaQubits in the order that they were added. You should not mutate this.
breakpoints
The breakpoints for the piecewise approximation.
Returns
The breakpoints for the piecewise approximation.
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.
data
The circuit data (instructions and context).
Returns
a list-like object containing the CircuitInstructions for each instruction.
Return type
QuantumCircuitData
degree
The degree of the polynomials.
Returns
The degree of the polynomials.
f_x
The function to be approximated.
Returns
The function to be approximated.
global_phase
The global phase of the current circuit scope in radians.
instances
Default value: 256
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.
metadata
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_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_parameters
The number of parameter objects in the circuit.
num_qubits
Return number of qubits.
num_state_qubits
The number of state qubits representing the state .
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 – When circuit is not scheduled.
parameters
The parameters defined in the circuit.
This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.
Examples
The snippet below shows that insertion order of parameters does not matter.
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
└─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])To respect numerical sorting, a ParameterVector can be used.
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
... circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
..., ParameterVectorElement(x[11])
])Returns
The sorted Parameter objects in the circuit.
polynomials
The polynomials for the piecewise approximation.
Returns
The polynomials for the piecewise approximation.
Raises
TypeError – If the input function is not in the correct format.
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.