LinearFunction#
- class qiskit.circuit.library.LinearFunction(linear, validate_input=False)[source]#
Bases:
GateA 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.
- প্যারামিটার:
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.
- রেইজেস:
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)[source]#
Extend linear function to a linear function over nq qubits, with identities on other subsystems.
- প্যারামিটার:
- রিটার্নস:
extended linear function.
- রিটার্ন টাইপ:
- function_str()[source]#
Return string representation of the linear function viewed as a linear transformation.
- is_permutation()[source]#
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.
- রিটার্ন টাইপ:
- mat_str()[source]#
Return string representation of the linear function viewed as a matrix with 0/1 entries.
- permutation_pattern()[source]#
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.