201 lines
7.2 KiB
Plaintext
201 lines
7.2 KiB
Plaintext
---
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title: LinearFunction
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description: API reference for qiskit.circuit.library.LinearFunction
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.LinearFunction
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---
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# LinearFunction
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<Class id="qiskit.circuit.library.LinearFunction" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/circuit/library/generalized_gates/linear_function.py" signature="qiskit.circuit.library.LinearFunction(linear, validate_input=False)" modifiers="class">
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Bases: [`Gate`](qiskit.circuit.Gate "qiskit.circuit.gate.Gate")
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A linear reversible circuit on n qubits.
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Internally, a linear function acting on n qubits is represented as a n x n matrix of 0s and 1s in numpy array format.
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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].
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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.
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**Example:** the circuit
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```python
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q_0: ──■──
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┌─┴─┐
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q_1: ┤ X ├
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└───┘
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q_2: ─────
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```
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is represented by a 3x3 linear matrix
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$$
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\begin{split}\begin{pmatrix}
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1 & 0 & 0 \\
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1 & 1 & 0 \\
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0 & 0 & 1
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\end{pmatrix}\end{split}
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$$
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**References:**
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\[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.](https://web.eecs.umich.edu/~imarkov/pubs/jour/qic08-cnot.pdf)
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Create a new linear function.
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**Parameters**
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* **LinearFunction** (*linear (*[*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")*\[*[*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")*] or ndarray\[*[*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")*] 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.
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* **validate\_input** – if True, performs more expensive input validation checks, such as checking that a given n x n matrix is invertible.
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**Raises**
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[**CircuitError**](circuit#qiskit.circuit.CircuitError "qiskit.circuit.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).
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.LinearFunction.condition_bits">
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Get Clbits in condition.
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.LinearFunction.decompositions">
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Get the decompositions of the instruction from the SessionEquivalenceLibrary.
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</Attribute>
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### definition
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<Attribute id="qiskit.circuit.library.LinearFunction.definition">
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Return definition in terms of other basic gates.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.LinearFunction.duration">
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Get the duration.
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</Attribute>
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### label
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<Attribute id="qiskit.circuit.library.LinearFunction.label">
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Return instruction label
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</Attribute>
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### linear
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<Attribute id="qiskit.circuit.library.LinearFunction.linear">
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Returns the n x n matrix representing this linear function.
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.LinearFunction.name">
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Return the name.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.LinearFunction.num_clbits">
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Return the number of clbits.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.LinearFunction.num_qubits">
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Return the number of qubits.
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</Attribute>
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### original\_circuit
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<Attribute id="qiskit.circuit.library.LinearFunction.original_circuit">
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Returns the original circuit used to construct this linear function (including None, when the linear function is not constructed from a circuit).
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</Attribute>
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### params
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<Attribute id="qiskit.circuit.library.LinearFunction.params">
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return instruction params.
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.LinearFunction.unit">
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Get the time unit of duration.
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</Attribute>
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## Methods
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### extend\_with\_identity
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<Function id="qiskit.circuit.library.LinearFunction.extend_with_identity" signature="extend_with_identity(num_qubits, positions)">
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Extend linear function to a linear function over nq qubits, with identities on other subsystems.
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**Parameters**
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* **num\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – number of qubits of the extended function.
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* **positions** ([*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")*]*) – describes the positions of original qubits in the extended function’s qubits.
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**Returns**
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extended linear function.
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**Return type**
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[LinearFunction](#qiskit.circuit.library.LinearFunction "qiskit.circuit.library.LinearFunction")
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</Function>
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### function\_str
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<Function id="qiskit.circuit.library.LinearFunction.function_str" signature="function_str()">
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Return string representation of the linear function viewed as a linear transformation.
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</Function>
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### is\_permutation
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<Function id="qiskit.circuit.library.LinearFunction.is_permutation" signature="is_permutation()">
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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.
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**Return type**
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[bool](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")
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</Function>
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### mat\_str
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<Function id="qiskit.circuit.library.LinearFunction.mat_str" signature="mat_str()">
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Return string representation of the linear function viewed as a matrix with 0/1 entries.
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</Function>
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### permutation\_pattern
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<Function id="qiskit.circuit.library.LinearFunction.permutation_pattern" signature="permutation_pattern()">
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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.
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</Function>
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### synthesize
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<Function id="qiskit.circuit.library.LinearFunction.synthesize" signature="synthesize()">
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Synthesizes the linear function into a quantum circuit.
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**Returns**
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A circuit implementing the evolution.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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</Function>
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### validate\_parameter
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<Function id="qiskit.circuit.library.LinearFunction.validate_parameter" signature="validate_parameter(parameter)">
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Parameter validation
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</Function>
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</Class>
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