432 lines
17 KiB
Plaintext
432 lines
17 KiB
Plaintext
---
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title: PauliTwoDesign (latest version)
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description: API reference for qiskit.circuit.library.PauliTwoDesign in the latest version of qiskit
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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.PauliTwoDesign
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---
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# PauliTwoDesign
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<Class id="qiskit.circuit.library.PauliTwoDesign" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/n_local/pauli_two_design.py#L24-L141" signature="qiskit.circuit.library.PauliTwoDesign(num_qubits=None, reps=3, seed=None, insert_barriers=False, name='PauliTwoDesign')" modifiers="class">
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Bases: [`TwoLocal`](qiskit.circuit.library.TwoLocal "qiskit.circuit.library.n_local.two_local.TwoLocal")
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The Pauli Two-Design ansatz.
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This class implements a particular form of a 2-design circuit \[1], which is frequently studied in quantum machine learning literature, such as e.g. the investigating of Barren plateaus in variational algorithms \[2].
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The circuit consists of alternating rotation and entanglement layers with an initial layer of $\sqrt{H} = RY(\pi/4)$ gates. The rotation layers contain single qubit Pauli rotations, where the axis is chosen uniformly at random to be X, Y or Z. The entanglement layers is compromised of pairwise CZ gates with a total depth of 2.
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For instance, the circuit could look like this (but note that choosing a different seed yields different Pauli rotations).
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```python
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┌─────────┐┌──────────┐ ░ ┌──────────┐ ░ ┌──────────┐
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q_0: ┤ RY(π/4) ├┤ RZ(θ[0]) ├─■─────░─┤ RY(θ[4]) ├─■─────░──┤ RZ(θ[8]) ├
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├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ├──────────┤
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q_1: ┤ RY(π/4) ├┤ RZ(θ[1]) ├─■──■──░─┤ RY(θ[5]) ├─■──■──░──┤ RX(θ[9]) ├
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├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ┌┴──────────┤
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q_2: ┤ RY(π/4) ├┤ RX(θ[2]) ├─■──■──░─┤ RY(θ[6]) ├─■──■──░─┤ RX(θ[10]) ├
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├─────────┤├──────────┤ │ ░ ├──────────┤ │ ░ ├───────────┤
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q_3: ┤ RY(π/4) ├┤ RZ(θ[3]) ├─■─────░─┤ RX(θ[7]) ├─■─────░─┤ RY(θ[11]) ├
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└─────────┘└──────────┘ ░ └──────────┘ ░ └───────────┘
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```
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**Examples**
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```python
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from qiskit.circuit.library import PauliTwoDesign
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circuit = PauliTwoDesign(4, reps=2, seed=5, insert_barriers=True)
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circuit.draw('mpl')
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```
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**References**
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**\[1]: Nakata et al., Unitary 2-designs from random X- and Z-diagonal unitaries.**
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[arXiv:1502.07514](https://arxiv.org/pdf/1502.07514.pdf)
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**\[2]: McClean et al., Barren plateaus in quantum neural network training landscapes.**
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[arXiv:1803.11173](https://arxiv.org/pdf/1803.11173.pdf)
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**Parameters**
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* **num\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)") *| None*) – The number of qubits of the Pauli Two-Design circuit.
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* **reps** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – Specifies how often a block consisting of a rotation layer and entanglement layer is repeated.
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* **seed** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)") *| None*) – The seed for randomly choosing the axes of the Pauli rotations.
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* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – If `True`, barriers are inserted in between each layer. If `False`, no barriers are inserted. Defaults to `False`.
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.ancillas">
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A list of `AncillaQubit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.calibrations">
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Return calibration dictionary.
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The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.clbits">
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A list of `Clbit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### data
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.data">
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The circuit data (instructions and context).
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**Returns**
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a list-like object containing the [`CircuitInstruction`](qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.
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**Return type**
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QuantumCircuitData
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</Attribute>
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### entanglement
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.entanglement">
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Get the entanglement strategy.
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**Returns**
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The entanglement strategy, see `get_entangler_map()` for more detail on how the format is interpreted.
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</Attribute>
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### entanglement\_blocks
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.entanglement_blocks">
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The blocks in the entanglement layers.
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**Returns**
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The blocks in the entanglement layers.
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</Attribute>
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### flatten
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.flatten">
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Returns whether the circuit is wrapped in nested gates/instructions or flattened.
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</Attribute>
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### global\_phase
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.global_phase">
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The global phase of the current circuit scope in radians.
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</Attribute>
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### initial\_state
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.initial_state">
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Return the initial state that is added in front of the n-local circuit.
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**Returns**
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The initial state.
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</Attribute>
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### insert\_barriers
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.insert_barriers">
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If barriers are inserted in between the layers or not.
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**Returns**
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`True`, if barriers are inserted in between the layers, `False` if not.
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</Attribute>
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### instances
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.instances" attributeValue="189" />
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### layout
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.layout">
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Return any associated layout information about the circuit
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This attribute contains an optional [`TranspileLayout`](qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation.
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There are two types of permutations caused by the [`transpile()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.
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</Attribute>
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### metadata
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.metadata">
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Arbitrary user-defined metadata for the circuit.
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Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.
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</Attribute>
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### num\_ancillas
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_ancillas">
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Return the number of ancilla qubits.
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</Attribute>
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### num\_captured\_vars
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_captured_vars">
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The number of real-time classical variables in the circuit marked as captured from an enclosing scope.
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This is the length of the `iter_captured_vars()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.PauliTwoDesign.num_input_vars "qiskit.circuit.library.PauliTwoDesign.num_input_vars") must be zero.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_clbits">
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Return number of classical bits.
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</Attribute>
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### num\_declared\_vars
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_declared_vars">
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The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.
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This is the length of the `iter_declared_vars()` iterable.
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</Attribute>
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### num\_input\_vars
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_input_vars">
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The number of real-time classical variables in the circuit marked as circuit inputs.
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This is the length of the `iter_input_vars()` iterable. If this is non-zero, [`num_captured_vars`](#qiskit.circuit.library.PauliTwoDesign.num_captured_vars "qiskit.circuit.library.PauliTwoDesign.num_captured_vars") must be zero.
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</Attribute>
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### num\_layers
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_layers">
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Return the number of layers in the n-local circuit.
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**Returns**
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The number of layers in the circuit.
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_parameters">
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The number of parameter objects in the circuit.
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</Attribute>
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### num\_parameters\_settable
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_parameters_settable">
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Return the number of settable parameters.
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**Returns**
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The number of possibly distinct parameters.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_qubits">
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Returns the number of qubits in this circuit.
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**Returns**
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The number of qubits.
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</Attribute>
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### num\_vars
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.num_vars">
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The number of real-time classical variables in the circuit.
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This is the length of the `iter_vars()` iterable.
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</Attribute>
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### op\_start\_times
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.op_start_times">
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Return a list of operation start times.
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This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.
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**Returns**
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List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.
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**Raises**
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[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError "(in Python v3.13)") – When circuit is not scheduled.
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</Attribute>
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### ordered\_parameters
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.ordered_parameters">
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The parameters used in the underlying circuit.
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This includes float values and duplicates.
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**Examples**
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```python
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>>> # prepare circuit ...
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>>> print(nlocal)
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┌───────┐┌──────────┐┌──────────┐┌──────────┐
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q_0: ┤ Ry(1) ├┤ Ry(θ[1]) ├┤ Ry(θ[1]) ├┤ Ry(θ[3]) ├
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└───────┘└──────────┘└──────────┘└──────────┘
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>>> nlocal.parameters
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{Parameter(θ[1]), Parameter(θ[3])}
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>>> nlocal.ordered_parameters
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[1, Parameter(θ[1]), Parameter(θ[1]), Parameter(θ[3])]
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```
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**Returns**
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The parameters objects used in the circuit.
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</Attribute>
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### parameter\_bounds
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.parameter_bounds">
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The parameter bounds for the unbound parameters in the circuit.
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**Returns**
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A list of pairs indicating the bounds, as (lower, upper). None indicates an unbounded parameter in the corresponding direction. If `None` is returned, problem is fully unbounded.
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</Attribute>
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### parameters
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.parameters">
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The parameters defined in the circuit.
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This attribute returns the [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.
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**Examples**
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The snippet below shows that insertion order of parameters does not matter.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter
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>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
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>>> circuit = QuantumCircuit(1)
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>>> circuit.rx(b, 0)
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>>> circuit.rz(elephant, 0)
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>>> circuit.ry(a, 0)
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>>> circuit.parameters # sorted alphabetically!
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ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
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```
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Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter
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>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
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>>> circuit = QuantumCircuit(1)
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>>> circuit.u(*angles, 0)
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>>> circuit.draw()
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┌─────────────────────────────┐
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q: ┤ U(angle_1,angle_2,angle_10) ├
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└─────────────────────────────┘
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>>> circuit.parameters
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ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
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```
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To respect numerical sorting, a [`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
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>>> x = ParameterVector("x", 12)
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>>> circuit = QuantumCircuit(1)
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>>> for x_i in x:
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... circuit.rx(x_i, 0)
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>>> circuit.parameters
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ParameterView([
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ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
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ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
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..., ParameterVectorElement(x[11])
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])
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```
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**Returns**
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The sorted [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.
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</Attribute>
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### preferred\_init\_points
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.preferred_init_points">
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The initial points for the parameters. Can be stored as initial guess in optimization.
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**Returns**
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The initial values for the parameters, or None, if none have been set.
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.prefix" attributeValue="'circuit'" />
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### qregs
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.qregs" attributeTypeHint="list[QuantumRegister]">
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A list of the `QuantumRegister`s in this circuit. You should not mutate this.
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</Attribute>
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### qubits
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.qubits">
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A list of `Qubit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### reps
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.reps">
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The number of times rotation and entanglement block are repeated.
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**Returns**
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The number of repetitions.
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</Attribute>
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### rotation\_blocks
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.rotation_blocks">
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The blocks in the rotation layers.
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**Returns**
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The blocks in the rotation layers.
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.name" attributeTypeHint="str">
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A human-readable name for the circuit.
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</Attribute>
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### cregs
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.cregs" attributeTypeHint="list[ClassicalRegister]">
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A list of the `ClassicalRegister`s in this circuit. You should not mutate this.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.duration" attributeTypeHint="int | float | None">
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The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.PauliTwoDesign.unit "qiskit.circuit.library.PauliTwoDesign.unit").
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.PauliTwoDesign.unit">
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The unit that [`duration`](#qiskit.circuit.library.PauliTwoDesign.duration "qiskit.circuit.library.PauliTwoDesign.duration") is specified in.
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</Attribute>
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</Class>
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