UniformDistribution

class UniformDistribution(num_qubits, name='P(X)')

Bases: QuantumCircuit

A circuit to encode a discretized uniform distribution in qubit amplitudes.

This simply corresponds to applying Hadamard gates on all qubits.

The probability density function of the discretized uniform distribution on \(N\) values is

\[\mathbb{P}(X = x) = \frac{1}{N}.\]

This circuit considers \(N = 2^n\), where \(n =\) num_qubits and prepares the state

\[\mathcal{P}_X |0\rangle^{\otimes n} = \frac{1}{\sqrt{2^n}} \sum_{x=0}^{2^n - 1} |x\rangle\]

Examples

>>> from qiskit_finance.circuit.library.probability_distributions import UniformDistribution
>>> circuit = UniformDistribution(3)
>>> circuit.decompose().draw()
     ┌───┐
q_0: ┤ H ├
     ├───┤
q_1: ┤ H ├
     ├───┤
q_2: ┤ H ├
     └───┘

Parameters:

• num_qubits (int) – The number of qubits in the circuit, the distribution is uniform over 2 ** num_qubits values.

• name (str) – The name of the circuit.

Attributes

Methods