LinearFunction
class qiskit.circuit.library.LinearFunction(linear, validate_input=False)
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
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
- 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.
Raises
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
extend_with_identity(num_qubits, positions)
Extend linear function to a linear function over nq qubits, with identities on other subsystems.
Parameters
- 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.
Returns
extended linear function.
Return type
function_str
function_str()
Return string representation of the linear function viewed as a linear transformation.
is_permutation
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
mat_str
mat_str()
Return string representation of the linear function viewed as a matrix with 0/1 entries.
permutation_pattern
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
synthesize()
Synthesizes the linear function into a quantum circuit.
Returns
A circuit implementing the evolution.
Return type
validate_parameter
validate_parameter(parameter)
Parameter validation