418 lines
15 KiB
Plaintext
418 lines
15 KiB
Plaintext
---
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title: Clifford
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description: API reference for qiskit.quantum_info.Clifford
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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.quantum_info.Clifford
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---
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# Clifford
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<Class id="qiskit.quantum_info.Clifford" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/quantum_info/operators/symplectic/clifford.py" signature="Clifford(data, validate=True)" modifiers="class">
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Bases: `qiskit.quantum_info.operators.base_operator.BaseOperator`, `qiskit.quantum_info.operators.mixins.adjoint.AdjointMixin`
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An N-qubit unitary operator from the Clifford group.
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**Representation**
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An *N*-qubit Clifford operator is stored as a length *2N* [`StabilizerTable`](qiskit.quantum_info.StabilizerTable "qiskit.quantum_info.StabilizerTable") using the convention from reference \[1].
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* Rows 0 to *N-1* are the *destabilizer* group generators
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* Rows *N* to *2N-1* are the *stabilizer* group generators.
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The internal [`StabilizerTable`](qiskit.quantum_info.StabilizerTable "qiskit.quantum_info.StabilizerTable") for the Clifford can be accessed using the [`table`](#qiskit.quantum_info.Clifford.table "qiskit.quantum_info.Clifford.table") attribute. The destabilizer or stabilizer rows can each be accessed as a length-N Stabilizer table using [`destabilizer`](#qiskit.quantum_info.Clifford.destabilizer "qiskit.quantum_info.Clifford.destabilizer") and [`stabilizer`](#qiskit.quantum_info.Clifford.stabilizer "qiskit.quantum_info.Clifford.stabilizer") attributes.
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A more easily human readable representation of the Clifford operator can be obtained by calling the [`to_dict()`](qiskit.quantum_info.Clifford#to_dict "qiskit.quantum_info.Clifford.to_dict") method. This representation is also used if a Clifford object is printed as in the following example
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```python
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from qiskit import QuantumCircuit
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from qiskit.quantum_info import Clifford
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# Bell state generation circuit
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qc = QuantumCircuit(2)
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qc.h(0)
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qc.cx(0, 1)
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cliff = Clifford(qc)
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# Print the Clifford
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print(cliff)
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# Print the Clifford destabilizer rows
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print(cliff.destabilizer)
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# Print the Clifford stabilizer rows
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print(cliff.stabilizer)
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```
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```python
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Clifford: Stabilizer = ['+XX', '+ZZ'], Destabilizer = ['+IZ', '+XI']
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StabilizerTable: ['+IZ', '+XI']
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StabilizerTable: ['+XX', '+ZZ']
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```
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**Circuit Conversion**
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Clifford operators can be initialized from circuits containing *only* the following Clifford gates: [`IGate`](qiskit.circuit.library.IGate "qiskit.circuit.library.IGate"), [`XGate`](qiskit.circuit.library.XGate "qiskit.circuit.library.XGate"), [`YGate`](qiskit.circuit.library.YGate "qiskit.circuit.library.YGate"), [`ZGate`](qiskit.circuit.library.ZGate "qiskit.circuit.library.ZGate"), [`HGate`](qiskit.circuit.library.HGate "qiskit.circuit.library.HGate"), [`SGate`](qiskit.circuit.library.SGate "qiskit.circuit.library.SGate"), [`SdgGate`](qiskit.circuit.library.SdgGate "qiskit.circuit.library.SdgGate"), [`CXGate`](qiskit.circuit.library.CXGate "qiskit.circuit.library.CXGate"), [`CZGate`](qiskit.circuit.library.CZGate "qiskit.circuit.library.CZGate"), [`SwapGate`](qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate"). They can be converted back into a [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit"), or [`Gate`](qiskit.circuit.Gate "qiskit.circuit.Gate") object using the [`to_circuit()`](qiskit.quantum_info.Clifford#to_circuit "qiskit.quantum_info.Clifford.to_circuit") or [`to_instruction()`](qiskit.quantum_info.Clifford#to_instruction "qiskit.quantum_info.Clifford.to_instruction") methods respectively. Note that this decomposition is not necessarily optimal in terms of number of gates.
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<Admonition title="Note" type="note">
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A minimally generating set of gates for Clifford circuits is the [`HGate`](qiskit.circuit.library.HGate "qiskit.circuit.library.HGate") and [`SGate`](qiskit.circuit.library.SGate "qiskit.circuit.library.SGate") gate and *either* the [`CXGate`](qiskit.circuit.library.CXGate "qiskit.circuit.library.CXGate") or [`CZGate`](qiskit.circuit.library.CZGate "qiskit.circuit.library.CZGate") two-qubit gate.
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</Admonition>
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Clifford operators can also be converted to [`Operator`](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator") objects using the [`to_operator()`](qiskit.quantum_info.Clifford#to_operator "qiskit.quantum_info.Clifford.to_operator") method. This is done via decomposing to a circuit, and then simulating the circuit as a unitary operator.
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**References**
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1. S. Aaronson, D. Gottesman, *Improved Simulation of Stabilizer Circuits*, Phys. Rev. A 70, 052328 (2004). [arXiv:quant-ph/0406196](https://arxiv.org/abs/quant-ph/0406196)
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Initialize an operator object.
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## Methods
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### adjoint
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<Function id="qiskit.quantum_info.Clifford.adjoint" signature="Clifford.adjoint()">
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Return the adjoint of the Operator.
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</Function>
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### compose
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<Function id="qiskit.quantum_info.Clifford.compose" signature="Clifford.compose(other, qargs=None, front=False)">
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Return the operator composition with another Clifford.
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**Parameters**
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* **other** ([*Clifford*](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")) – a Clifford object.
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* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
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* **front** (*bool*) – If True compose using right operator multiplication, instead of left multiplication \[default: False].
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**Returns**
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The composed Clifford.
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**Return type**
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[Clifford](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")
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**Raises**
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**QiskitError** – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
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<Admonition title="Note" type="note">
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Composition (`&`) by default is defined as left matrix multiplication for matrix operators, while [`dot()`](qiskit.quantum_info.Clifford#dot "qiskit.quantum_info.Clifford.dot") is defined as right matrix multiplication. That is that `A & B == A.compose(B)` is equivalent to `B.dot(A)` when `A` and `B` are of the same type.
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Setting the `front=True` kwarg changes this to right matrix multiplication and is equivalent to the [`dot()`](qiskit.quantum_info.Clifford#dot "qiskit.quantum_info.Clifford.dot") method `A.dot(B) == A.compose(B, front=True)`.
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</Admonition>
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</Function>
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### conjugate
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<Function id="qiskit.quantum_info.Clifford.conjugate" signature="Clifford.conjugate()">
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Return the conjugate of the Clifford.
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</Function>
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### copy
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<Function id="qiskit.quantum_info.Clifford.copy" signature="Clifford.copy()">
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Make a deep copy of current operator.
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</Function>
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### dot
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<Function id="qiskit.quantum_info.Clifford.dot" signature="Clifford.dot(other, qargs=None)">
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Return the right multiplied operator self \* other.
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**Parameters**
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* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator object.
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* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
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**Returns**
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The right matrix multiplied Operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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</Function>
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### expand
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<Function id="qiskit.quantum_info.Clifford.expand" signature="Clifford.expand(other)">
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Return the reverse-order tensor product with another Clifford.
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**Parameters**
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**other** ([*Clifford*](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")) – a Clifford object.
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**Returns**
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**the tensor product $b \otimes a$, where $a$**
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is the current Clifford, and $b$ is the other Clifford.
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**Return type**
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[Clifford](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")
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</Function>
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### from\_circuit
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<Function id="qiskit.quantum_info.Clifford.from_circuit" signature="Clifford.from_circuit(circuit)" modifiers="static">
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Initialize from a QuantumCircuit or Instruction.
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**Parameters**
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**circuit** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *or*[*Instruction*](qiskit.circuit.Instruction "qiskit.circuit.Instruction")) – instruction to initialize.
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**Returns**
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the Clifford object for the instruction.
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**Return type**
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[Clifford](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")
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**Raises**
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**QiskitError** – if the input instruction is non-Clifford or contains classical register instruction.
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</Function>
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### from\_dict
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<Function id="qiskit.quantum_info.Clifford.from_dict" signature="Clifford.from_dict(obj)" modifiers="static">
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Load a Clifford from a dictionary
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</Function>
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### from\_label
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<Function id="qiskit.quantum_info.Clifford.from_label" signature="Clifford.from_label(label)" modifiers="static">
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Return a tensor product of single-qubit Clifford gates.
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**Parameters**
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**label** (*string*) – single-qubit operator string.
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**Returns**
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The N-qubit Clifford operator.
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**Return type**
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[Clifford](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")
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**Raises**
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**QiskitError** – if the label contains invalid characters.
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#### Additional Information:
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The labels correspond to the single-qubit Cliffords are
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* * Label
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* Stabilizer
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* Destabilizer
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* * `"I"`
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* +Z
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* +X
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* * `"X"`
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* -Z
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* +X
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* * `"Y"`
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* -Z
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* -X
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* * `"Z"`
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* +Z
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* -X
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* * `"H"`
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* +X
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* +Z
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* * `"S"`
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* +Z
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* +Y
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</Function>
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### input\_dims
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<Function id="qiskit.quantum_info.Clifford.input_dims" signature="Clifford.input_dims(qargs=None)">
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Return tuple of input dimension for specified subsystems.
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</Function>
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### is\_unitary
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<Function id="qiskit.quantum_info.Clifford.is_unitary" signature="Clifford.is_unitary()">
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Return True if the Clifford table is valid.
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</Function>
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### output\_dims
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<Function id="qiskit.quantum_info.Clifford.output_dims" signature="Clifford.output_dims(qargs=None)">
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Return tuple of output dimension for specified subsystems.
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</Function>
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### power
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<Function id="qiskit.quantum_info.Clifford.power" signature="Clifford.power(n)">
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Return the compose of a operator with itself n times.
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**Parameters**
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**n** (*int*) – the number of times to compose with self (n>0).
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**Returns**
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the n-times composed operator.
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**Return type**
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[Pauli](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")
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**Raises**
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**QiskitError** – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.
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</Function>
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### reshape
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<Function id="qiskit.quantum_info.Clifford.reshape" signature="Clifford.reshape(input_dims=None, output_dims=None, num_qubits=None)">
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Return a shallow copy with reshaped input and output subsystem dimensions.
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**Parameters**
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* **input\_dims** (*None or tuple*) – new subsystem input dimensions. If None the original input dims will be preserved \[Default: None].
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* **output\_dims** (*None or tuple*) – new subsystem output dimensions. If None the original output dims will be preserved \[Default: None].
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* **num\_qubits** (*None or int*) – reshape to an N-qubit operator \[Default: None].
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**Returns**
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returns self with reshaped input and output dimensions.
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**Return type**
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BaseOperator
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**Raises**
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**QiskitError** – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.
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</Function>
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### tensor
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<Function id="qiskit.quantum_info.Clifford.tensor" signature="Clifford.tensor(other)">
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Return the tensor product with another Clifford.
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**Parameters**
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**other** ([*Clifford*](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")) – a Clifford object.
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**Returns**
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**the tensor product $a \otimes b$, where $a$**
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is the current Clifford, and $b$ is the other Clifford.
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**Return type**
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[Clifford](qiskit.quantum_info.Clifford "qiskit.quantum_info.Clifford")
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<Admonition title="Note" type="note">
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The tensor product can be obtained using the `^` binary operator. Hence `a.tensor(b)` is equivalent to `a ^ b`.
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</Admonition>
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</Function>
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### to\_circuit
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<Function id="qiskit.quantum_info.Clifford.to_circuit" signature="Clifford.to_circuit()">
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Return a QuantumCircuit implementing the Clifford.
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For N \<= 3 qubits this is based on optimal CX cost decomposition from reference \[1]. For N > 3 qubits this is done using the general non-optimal compilation routine from reference \[2].
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**Returns**
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a circuit implementation of the Clifford.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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**References**
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1. S. Bravyi, D. Maslov, *Hadamard-free circuits expose the structure of the Clifford group*, [arXiv:2003.09412 \[quant-ph\]](https://arxiv.org/abs/2003.09412)
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2. S. Aaronson, D. Gottesman, *Improved Simulation of Stabilizer Circuits*, Phys. Rev. A 70, 052328 (2004). [arXiv:quant-ph/0406196](https://arxiv.org/abs/quant-ph/0406196)
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</Function>
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### to\_dict
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<Function id="qiskit.quantum_info.Clifford.to_dict" signature="Clifford.to_dict()">
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Return dictionary representation of Clifford object.
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</Function>
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### to\_instruction
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<Function id="qiskit.quantum_info.Clifford.to_instruction" signature="Clifford.to_instruction()">
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Return a Gate instruction implementing the Clifford.
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</Function>
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### to\_matrix
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<Function id="qiskit.quantum_info.Clifford.to_matrix" signature="Clifford.to_matrix()">
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Convert operator to Numpy matrix.
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</Function>
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### to\_operator
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<Function id="qiskit.quantum_info.Clifford.to_operator" signature="Clifford.to_operator()">
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Convert to an Operator object.
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</Function>
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### transpose
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<Function id="qiskit.quantum_info.Clifford.transpose" signature="Clifford.transpose()">
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Return the transpose of the Clifford.
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</Function>
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## Attributes
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### destabilizer
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<Attribute id="qiskit.quantum_info.Clifford.destabilizer">
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Return the destabilizer block of the StabilizerTable.
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</Attribute>
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### dim
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<Attribute id="qiskit.quantum_info.Clifford.dim">
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Return tuple (input\_shape, output\_shape).
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.quantum_info.Clifford.num_qubits">
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Return the number of qubits if a N-qubit operator or None otherwise.
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</Attribute>
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### qargs
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<Attribute id="qiskit.quantum_info.Clifford.qargs">
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Return the qargs for the operator.
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</Attribute>
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### settings
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<Attribute id="qiskit.quantum_info.Clifford.settings">
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Return operator settings.
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</Attribute>
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### stabilizer
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<Attribute id="qiskit.quantum_info.Clifford.stabilizer">
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Return the stabilizer block of the StabilizerTable.
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</Attribute>
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### table
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<Attribute id="qiskit.quantum_info.Clifford.table">
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Return StabilizerTable
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</Attribute>
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</Class>
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