74 lines
4.5 KiB
Plaintext
74 lines
4.5 KiB
Plaintext
---
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title: pauli_two_design (latest version)
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description: API reference for qiskit.circuit.library.pauli_two_design 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.pauli_two_design
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---
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<span id="pauli-two-design" />
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# pauli\_two\_design
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<Class id="qiskit.circuit.library.pauli_two_design" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/n_local/pauli_two_design.py#L25-L112" signature="qiskit.circuit.library.pauli_two_design(num_qubits, reps=3, seed=None, insert_barriers=False, parameter_prefix='θ', name='PauliTwoDesign')" modifiers="class">
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Bases:
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Construct a Pauli 2-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 investigation 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:
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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 pauli_two_design
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circuit = pauli_two_design(4, reps=2, seed=5, insert_barriers=True)
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circuit.draw("mpl")
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```
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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)")) – 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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* **parameter\_prefix** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – The prefix used for the rotation parameters.
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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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* **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – The circuit name.
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**Returns**
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A Pauli 2-design circuit.
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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]: 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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</Class>
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