QuadraticForm

class qiskit.circuit.library.QuadraticForm(num_result_qubits=None, quadratic=None, linear=None, offset=None, little_endian=True)

Bases: QuantumCircuit

Implements a quadratic form on binary variables encoded in qubit registers.

A quadratic form on binary variables is a quadratic function $Q$ acting on a binary variable of $n$ bits, $x = x_0 ... x_{n-1}$. For an integer matrix $A$, an integer vector $b$ and an integer $c$ the function can be written as

If $A$, $b$ or $c$ contain scalar values, this circuit computes only an approximation of the quadratic form.

Provided with $m$ qubits to encode the value, this circuit computes $Q(x) \mod 2^m$ in [two’s complement](https://stackoverflow.com/questions/1049722/what-is-twos-complement) representation.

Since we use two’s complement e.g. the value of $Q(x) = 3$ 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, $Q(x) = -3$ 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 $Q(x)$ is too large to be represented with m qubits, the resulting bitstring is $(Q(x) + 2^m) \mod 2^m)$.

The implementation of this circuit is discussed in [1], Fig. 6.

References

[1]: Gilliam et al., Grover Adaptive Search for Constrained Polynomial Binary Optimization.

arXiv:1912.04088

Parameters

• num_result_qubits (Optional[int]) – The number of qubits to encode the result. Called $m$ in the class documentation.
• quadratic (Optional[Union[np.ndarray, List[List[Union[float, ParameterExpression]]]]]) – A matrix containing the quadratic coefficients, $A$.
• linear (Optional[Union[np.ndarray, List[Union[float, ParameterExpression]]]]) – An array containing the linear coefficients, $b$.
• offset (Optional[Union[float, ParameterExpression]]) – A constant offset, $c$.
• little_endian (bool) – Encode the result in little endianness.

Raises

• ValueError – If linear and quadratic have mismatching sizes.
• ValueError – If num_result_qubits is unspecified but cannot be determined because some values of the quadratic form are parameterized.

Attributes

name

from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)

my_circuit

Methods

required_result_qubits