152 lines
6.3 KiB
Plaintext
152 lines
6.3 KiB
Plaintext
---
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title: TwoQubitWeylDecomposition (dev version)
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description: API reference for qiskit.synthesis.TwoQubitWeylDecomposition in the dev 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.synthesis.TwoQubitWeylDecomposition
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---
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# TwoQubitWeylDecomposition
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<Class id="qiskit.synthesis.TwoQubitWeylDecomposition" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/main/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L105-L265" signature="qiskit.synthesis.TwoQubitWeylDecomposition(unitary_matrix, fidelity=0.999999999, *, _specialization=None)" modifiers="class">
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Bases: [`object`](https://docs.python.org/3/library/functions.html#object "(in Python v3.13)")
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Two-qubit Weyl decomposition.
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Decompose two-qubit unitary
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$$
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U = ({K_1}^l \otimes {K_1}^r) e^{(i a XX + i b YY + i c ZZ)} ({K_2}^l \otimes {K_2}^r)
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$$
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where
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$$
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U \in U(4),~
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{K_1}^l, {K_1}^r, {K_2}^l, {K_2}^r \in SU(2)
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$$
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and we stay in the “Weyl Chamber”
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$$
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\pi /4 \geq a \geq b \geq |c|
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$$
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This class avoids some problems of numerical instability near high-symmetry loci within the Weyl chamber. If there is a high-symmetry gate “nearby” (in terms of the requested average gate fidelity), then it return a canonicalized decomposition of that high-symmetry gate.
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**References**
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1. Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D. & Gambetta, J. M., *Validating quantum computers using randomized model circuits*, [arXiv:1811.12926 \[quant-ph\]](https://arxiv.org/abs/1811.12926)
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2. B. Kraus, J. I. Cirac, *Optimal Creation of Entanglement Using a Two-Qubit Gate*, [arXiv:0011050 \[quant-ph\]](https://arxiv.org/abs/quant-ph/0011050)
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3. B. Drury, P. J. Love, *Constructive Quantum Shannon Decomposition from Cartan Involutions*, [arXiv:0806.4015 \[quant-ph\]](https://arxiv.org/abs/0806.4015)
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## Attributes
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**Parameters**
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* **unitary\_matrix** ([*ndarray*](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.2)")) –
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* **fidelity** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)") *| None*) –
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* **\_specialization** (*two\_qubit\_decompose.Specialization | None*) –
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### a
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.a" attributeTypeHint="float" />
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### b
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.b" attributeTypeHint="float" />
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### c
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.c" attributeTypeHint="float" />
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### global\_phase
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.global_phase" attributeTypeHint="float" />
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### K1l
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K1l" attributeTypeHint="ndarray" />
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### K2l
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K2l" attributeTypeHint="ndarray" />
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### K1r
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K1r" attributeTypeHint="ndarray" />
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### K2r
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K2r" attributeTypeHint="ndarray" />
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### unitary\_matrix
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.unitary_matrix" attributeTypeHint="ndarray" />
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### requested\_fidelity
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.requested_fidelity" attributeTypeHint="float | None" />
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### calculated\_fidelity
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<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.calculated_fidelity" attributeTypeHint="float" />
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## Methods
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### actual\_fidelity
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<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.actual_fidelity" github="https://github.com/Qiskit/qiskit/tree/main/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L212-L216" signature="actual_fidelity(**kwargs)">
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Calculates the actual fidelity of the decomposed circuit to the input unitary.
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**Return type**
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[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")
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</Function>
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### circuit
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<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.circuit" github="https://github.com/Qiskit/qiskit/tree/main/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L203-L210" signature="circuit(*, euler_basis=None, simplify=False, atol=1e-12)">
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Returns Weyl decomposition in circuit form.
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**Parameters**
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* **euler\_basis** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)") *| None*) –
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* **simplify** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) –
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* **atol** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")) –
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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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### from\_bytes
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<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.from_bytes" github="https://github.com/Qiskit/qiskit/tree/main/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L244-L259" signature="from_bytes(bytes_in, *, requested_fidelity, _specialization=None, **kwargs)" modifiers="classmethod">
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Decode bytes into [`TwoQubitWeylDecomposition`](#qiskit.synthesis.TwoQubitWeylDecomposition "qiskit.synthesis.TwoQubitWeylDecomposition").
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**Parameters**
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* **bytes\_in** ([*bytes*](https://docs.python.org/3/library/stdtypes.html#bytes "(in Python v3.13)")) –
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* **requested\_fidelity** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")) –
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* **\_specialization** (*two\_qubit\_decompose.Specialization | None*) –
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**Return type**
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[TwoQubitWeylDecomposition](#qiskit.synthesis.TwoQubitWeylDecomposition "qiskit.synthesis.TwoQubitWeylDecomposition")
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</Function>
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### specialize
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<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.specialize" github="https://github.com/Qiskit/qiskit/tree/main/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L194-L201" signature="specialize()">
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Make changes to the decomposition to comply with any specializations.
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This method will always raise a `NotImplementedError` because there are no specializations to comply with in the current implementation.
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<Admonition title="Deprecated since version 1.1.0" type="danger">
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The method `qiskit.synthesis.two_qubit.two_qubit_decompose.TwoQubitWeylDecomposition.specialize()` is deprecated as of Qiskit 1.1.0. It will be removed in the 2.0.0 release.
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</Admonition>
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</Function>
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</Class>
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