QuadraticForm
class QuadraticForm(num_result_qubits=None, quadratic=None, linear=None, offset=None, little_endian=True)
Bases: qiskit.circuit.quantumcircuit.QuantumCircuit
Implements a quadratic form on binary variables encoded in qubit registers.
A quadratic form on binary variables is a quadratic function acting on a binary variable of bits, . For an integer matrix , an integer vector and an integer the function can be written as
If , or contain scalar values, this circuit computes only an approximation of the quadratic form.
Provided with qubits to encode the value, this circuit computes in [two’s complement](https://stackoverflow.com/questions/1049722/what-is-2s-complement) representation.
Since we use two’s complement e.g. the value of requires 2 bits to represent the value and 1 bit for the sign: 3 = ‘011’ where the first 0 indicates a positive value. On the other hand, would be -3 = ‘101’, where the first 1 indicates a negative value and 01 is the two’s complement of 3.
If the value of is too large to be represented with m qubits, the resulting bitstring is .
The implementation of this circuit is discussed in [1], Fig. 6.
References
[1]: Gilliam et al., Grover Adaptive Search for Constrained Polynomial Binary Optimization.
Parameters
- num_result_qubits (
Optional[int]) – The number of qubits to encode the result. Called in the class documentation. - quadratic (
Union[ndarray,List[List[Union[float,ParameterExpression]]],None]) – A matrix containing the quadratic coefficients, . - linear (
Union[ndarray,List[Union[float,ParameterExpression]],None]) – An array containing the linear coefficients, . - offset (
Union[float,ParameterExpression,None]) – A constant offset, . - little_endian (
bool) – Encode the result in little endianness.
Raises
- ValueError – If
linearandquadratichave mismatching sizes. - ValueError – If
num_result_qubitsis unspecified but cannot be determined because some values of the quadratic form are parameterized.
Methods Defined Here
required_result_qubits
static QuadraticForm.required_result_qubits(quadratic, linear, offset)
Get the number of required result qubits.
Parameters
- quadratic (
Union[ndarray,List[List[float]]]) – A matrix containing the quadratic coefficients. - linear (
Union[ndarray,List[float]]) – An array containing the linear coefficients. - offset (
float) – A constant offset.
Return type
int
Returns
The number of qubits needed to represent the value of the quadratic form in twos complement.
Attributes
ancillas
Returns a list of ancilla bits in the order that the registers were added.
Return type
List[AncillaQubit]
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
data
Return the circuit data (instructions and context).
Returns
a list-like object containing the CircuitInstructions for each instruction.
Return type
QuantumCircuitData
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 2603
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
The number of parameter objects in the circuit.
Return type
int
num_qubits
Return number of qubits.
Return type
int
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
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 unituitive 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])
])Return type
ParameterView
Returns
The sorted Parameter objects in the circuit.
prefix
Default value: 'circuit'