PiecewiseChebyshev¶
- class PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')[source]¶
Bases:
qiskit.circuit.library.blueprintcircuit.BlueprintCircuit
Piecewise Chebyshev approximation to an input function.
For a given function \(f(x)\) and degree \(d\), this class implements a piecewise polynomial Chebyshev approximation on \(n\) qubits to \(f(x)\) on the given intervals. All the polynomials in the approximation are of degree \(d\).
The values of the parameters are calculated according to [1].
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
- Parameters
f_x (
Union
[float
,Callable
[[int
],float
]]) – the function to be approximated. Constant functions should be specified as f_x = constant.degree (
Optional
[int
]) – the degree of the polynomials. Defaults to1
.breakpoints (
Optional
[List
[int
]]) – the breakpoints to define the piecewise-linear function. Defaults to the full interval.num_state_qubits (
Optional
[int
]) – number of qubits representing the state.name (
str
) – The name of the circuit object.
Attributes
- ancillas¶
Returns a list of ancilla bits in the order that the registers were added.
- Return type
List
[AncillaQubit
]
- breakpoints¶
The breakpoints for the piecewise approximation.
- Return type
List
[int
]- 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}}
- Return type
dict
- clbits¶
Returns a list of classical bits in the order that the registers were added.
- Return type
List
[Clbit
]
- data¶
- degree¶
The degree of the polynomials.
- Return type
int
- Returns
The degree of the polynomials.
- extension_lib = 'include "qelib1.inc";'¶
- f_x¶
The function to be approximated.
- Return type
Union
[float
,Callable
[[int
],float
]]- Returns
The function to be approximated.
- global_phase¶
Return the global phase of the circuit in radians.
- Return type
Union
[ParameterExpression
,float
]
- header = 'OPENQASM 2.0;'¶
- instances = 9¶
- 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_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 \(|x\rangle\).
- Return type
int
- Returns
The number of state qubits.
- parameters¶
- Return type
ParameterView
- polynomials¶
The polynomials for the piecewise approximation.
- Return type
List
[List
[float
]]- Returns
The polynomials for the piecewise approximation.
- Raises
TypeError – If the input function is not in the correct format.
- prefix = 'circuit'¶
- qregs¶
A list of the quantum registers associated with the circuit.