LinearFunction
class LinearFunction(linear, validate_input=False)
Bases: qiskit.circuit.gate.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
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.
Parameters
- 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.
Raises
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
LinearFunction.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.
Return type
bool
permutation_pattern
LinearFunction.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
LinearFunction.synthesize()
Synthesizes the linear function into a quantum circuit.
Returns
A circuit implementing the evolution.
Return type
validate_parameter
LinearFunction.validate_parameter(parameter)
Parameter validation
Attributes
condition_bits
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
Return type
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.