# LinearFunction¶

class LinearFunction(linear, validate_input=False)[fuente]

Bases: Gate

A linear reversible circuit on n qubits.

Internally, a linear function acting on n qubits is represented as a n x n matrix of 0s and 1s in numpy array format.

A linear function can be synthesized into CX and SWAP gates using the Patel–Markov–Hayes algorithm, as implemented in cnot_synth() based on reference [1].

For efficiency, the internal n x n matrix is stored in the format expected by cnot_synth, which is the big-endian (and not the little-endian) bit-ordering convention.

Example: the circuit

q_0: ──■──
┌─┴─┐
q_1: ┤ X ├
└───┘
q_2: ─────


is represented by a 3x3 linear matrix

$\begin{split}\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\end{split}$

References:

[1] Ketan N. Patel, Igor L. Markov, and John P. Hayes, Optimal synthesis of linear reversible circuits, Quantum Inf. Comput. 8(3) (2008). Online at umich.edu.

Create a new linear function.

Parámetros
• linear (list[list] or ndarray[bool] or QuantumCircuit) – either an n x n matrix, describing the linear function, or a quantum circuit composed of linear gates only (currently supported gates are CX and SWAP).

• validate_input (Optional[bool]) – if True, performs more expensive input validation checks, such as checking that a given n x n matrix is invertible.

Muestra

CircuitError – if the input is invalid: either a matrix is non {square, invertible}, or a quantum circuit contains non-linear gates.

Methods Defined Here

 is_permutation Returns whether this linear function is a permutation, that is whether every row and every column of the n x n matrix has exactly one 1. permutation_pattern This method first checks if a linear function is a permutation and raises a qiskit.circuit.exceptions.CircuitError if not. synthesize Synthesizes the linear function into a quantum circuit. validate_parameter Parameter validation

Attributes

condition_bits

Get Clbits in condition.

Tipo del valor devuelto

List[Clbit]

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

duration

Get the duration.

label

Return instruction label

Tipo del valor devuelto

str

linear

Returns the n x n matrix representing this linear function

name

Return the name.

num_clbits

Return the number of clbits.

num_qubits

Return the number of qubits.

original_circuit

Returns the original circuit used to construct this linear function (including None, when the linear function is not constructed from a circuit).

params

return instruction params.

unit

Get the time unit of duration.