134 lines
5.3 KiB
Plaintext
134 lines
5.3 KiB
Plaintext
---
|
|
title: TwoQubitWeylDecomposition
|
|
description: API reference for qiskit.synthesis.TwoQubitWeylDecomposition
|
|
in_page_toc_min_heading_level: 1
|
|
python_api_type: class
|
|
python_api_name: qiskit.synthesis.TwoQubitWeylDecomposition
|
|
---
|
|
|
|
# TwoQubitWeylDecomposition
|
|
|
|
<Class id="qiskit.synthesis.TwoQubitWeylDecomposition" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L131-L294" signature="qiskit.synthesis.TwoQubitWeylDecomposition(unitary_matrix, fidelity=0.999999999, *, _specialization=None)" modifiers="class">
|
|
Bases: [`object`](https://docs.python.org/3/library/functions.html#object "(in Python v3.12)")
|
|
|
|
Two-qubit Weyl decomposition.
|
|
|
|
Decompose two-qubit unitary
|
|
|
|
$$
|
|
U = ({K_1}^l \otimes {K_1}^r) e^{(i a XX + i b YY + i c ZZ)} ({K_2}^l \otimes {K_2}^r)
|
|
$$
|
|
|
|
where
|
|
|
|
$$
|
|
U \in U(4),~
|
|
{K_1}^l, {K_1}^r, {K_2}^l, {K_2}^r \in SU(2)
|
|
$$
|
|
|
|
and we stay in the “Weyl Chamber”
|
|
|
|
$$
|
|
\pi /4 \geq a \geq b \geq |c|
|
|
$$
|
|
|
|
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.
|
|
|
|
**References**
|
|
|
|
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)
|
|
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)
|
|
3. B. Drury, P. J. Love, *Constructive Quantum Shannon Decomposition from Cartan Involutions*, [arXiv:0806.4015 \[quant-ph\]](https://arxiv.org/abs/0806.4015)
|
|
|
|
## Attributes
|
|
|
|
### a
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.a" attributeTypeHint="float" />
|
|
|
|
### b
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.b" attributeTypeHint="float" />
|
|
|
|
### c
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.c" attributeTypeHint="float" />
|
|
|
|
### global\_phase
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.global_phase" attributeTypeHint="float" />
|
|
|
|
### K1l
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K1l" attributeTypeHint="ndarray" />
|
|
|
|
### K2l
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K2l" attributeTypeHint="ndarray" />
|
|
|
|
### K1r
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K1r" attributeTypeHint="ndarray" />
|
|
|
|
### K2r
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.K2r" attributeTypeHint="ndarray" />
|
|
|
|
### unitary\_matrix
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.unitary_matrix" attributeTypeHint="ndarray" />
|
|
|
|
### requested\_fidelity
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.requested_fidelity" attributeTypeHint="float | None" />
|
|
|
|
### calculated\_fidelity
|
|
|
|
<Attribute id="qiskit.synthesis.TwoQubitWeylDecomposition.calculated_fidelity" attributeTypeHint="float" />
|
|
|
|
## Methods
|
|
|
|
### actual\_fidelity
|
|
|
|
<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.actual_fidelity" github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L241-L245" signature="actual_fidelity(**kwargs)">
|
|
Calculates the actual fidelity of the decomposed circuit to the input unitary.
|
|
|
|
**Return type**
|
|
|
|
[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")
|
|
</Function>
|
|
|
|
### circuit
|
|
|
|
<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.circuit" github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L229-L239" signature="circuit(*, euler_basis=None, simplify=False, atol=1e-12)">
|
|
Returns Weyl decomposition in circuit form.
|
|
|
|
**Return type**
|
|
|
|
[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
|
|
</Function>
|
|
|
|
### from\_bytes
|
|
|
|
<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.from_bytes" github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L273-L288" signature="from_bytes(bytes_in, *, requested_fidelity, _specialization=None, **kwargs)" modifiers="classmethod">
|
|
Decode bytes into [`TwoQubitWeylDecomposition`](#qiskit.synthesis.TwoQubitWeylDecomposition "qiskit.synthesis.TwoQubitWeylDecomposition").
|
|
|
|
**Return type**
|
|
|
|
[TwoQubitWeylDecomposition](#qiskit.synthesis.TwoQubitWeylDecomposition "qiskit.synthesis.TwoQubitWeylDecomposition")
|
|
</Function>
|
|
|
|
### specialize
|
|
|
|
<Function id="qiskit.synthesis.TwoQubitWeylDecomposition.specialize" github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/utils/deprecation.py#L220-L227" signature="specialize()">
|
|
Make changes to the decomposition to comply with any specializations.
|
|
|
|
This method will always raise a `NotImplementedError` because there are no specializations to comply with in the current implementation.
|
|
|
|
<Admonition title="Deprecated since version 1.1.0" type="danger">
|
|
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.
|
|
</Admonition>
|
|
</Function>
|
|
</Class>
|
|
|