LinearFunction

class qiskit.circuit.library.LinearFunction(linear, validate_input=False)

ベースクラス: 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.

パラメータ:

• LinearFunction (linear (list[list] or ndarray[bool] or QuantumCircuit or) – or PermutationGate or Clifford): data from which a linear function can be constructed. It can be either a nxn matrix (describing the linear transformation), a permutation (which is a special case of a linear function), another linear function, a clifford (when it corresponds to a linear function), or a quantum circuit composed of linear gates (CX and SWAP) and other objects described above, including nested subcircuits.

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

例外:

CircuitError – if the input is invalid: either the input matrix is not square or not invertible, or the input quantum circuit contains non-linear objects (for example, a Hadamard gate, or a Clifford that does not correspond to a linear function).

Attributes

condition_bits

Get Clbits in condition.

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

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.

Methods

extend_with_identity(num_qubits, positions)

Extend linear function to a linear function over nq qubits, with identities on other subsystems.

パラメータ:

• num_qubits (int) – number of qubits of the extended function.

• positions (list[int]) – describes the positions of original qubits in the extended function’s qubits.

戻り値:

extended linear function.

戻り値の型:

LinearFunction

function_str()

Return string representation of the linear function viewed as a linear transformation.

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.

戻り値の型:

bool

mat_str()

Return string representation of the linear function viewed as a matrix with 0/1 entries.

permutation_pattern()

This method first checks if a linear function is a permutation and raises a qiskit.circuit.exceptions.CircuitError if not. In the case that this linear function is a permutation, returns the permutation pattern.

synthesize()

Synthesizes the linear function into a quantum circuit.

戻り値:

A circuit implementing the evolution.

戻り値の型:

QuantumCircuit

validate_parameter(parameter)

Parameter validation