110 lines
7.0 KiB
Plaintext
110 lines
7.0 KiB
Plaintext
---
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title: TwoQubitBasisDecomposer (v1.2)
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description: API reference for qiskit.synthesis.TwoQubitBasisDecomposer in qiskit v1.2
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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.TwoQubitBasisDecomposer
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---
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# TwoQubitBasisDecomposer
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<Class id="qiskit.synthesis.TwoQubitBasisDecomposer" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L497-L699" signature="qiskit.synthesis.TwoQubitBasisDecomposer(gate, basis_fidelity=1.0, euler_basis='U', pulse_optimize=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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A class for decomposing 2-qubit unitaries into minimal number of uses of a 2-qubit basis gate.
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**Parameters**
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* **gate** ([*Gate*](qiskit.circuit.Gate "qiskit.circuit.Gate")) – Two-qubit gate to be used in the KAK decomposition.
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* **basis\_fidelity** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")) – Fidelity to be assumed for applications of KAK Gate. Defaults to `1.0`.
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* **euler\_basis** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – Basis string to be provided to [`OneQubitEulerDecomposer`](qiskit.synthesis.OneQubitEulerDecomposer "qiskit.synthesis.OneQubitEulerDecomposer") for 1Q synthesis. Valid options are \[`'ZYZ'`, `'ZXZ'`, `'XYX'`, `'U'`, `'U3'`, `'U1X'`, `'PSX'`, `'ZSX'`, `'RR'`].
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* **pulse\_optimize** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)") *| None*) – If `True`, try to do decomposition which minimizes local unitaries in between entangling gates. This will raise an exception if an optimal decomposition is not implemented. Currently, only \[\{CX, SX, RZ}] is known. If `False`, don’t attempt optimization. If `None`, attempt optimization but don’t raise if unknown.
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### \_\_call\_\_
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.__call__" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L613-L692" signature="__call__(unitary, basis_fidelity=None, approximate=True, use_dag=False, *, _num_basis_uses=None)">
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Decompose a two-qubit `unitary` over fixed basis and $SU(2)$ using the best approximation given that each basis application has a finite `basis_fidelity`.
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**Parameters**
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* **unitary** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator") *or ndarray*) – $4 \times 4$ unitary to synthesize.
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* **basis\_fidelity** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)") *or None*) – Fidelity to be assumed for applications of KAK Gate. If given, overrides `basis_fidelity` given at init.
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* **approximate** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – Approximates if basis fidelities are less than 1.0.
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* **use\_dag** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – If true a [`DAGCircuit`](qiskit.dagcircuit.DAGCircuit "qiskit.dagcircuit.DAGCircuit") is returned instead of a `QuantumCircuit` when this class is called.
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* **\_num\_basis\_uses** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – force a particular approximation by passing a number in \[0, 3].
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**Returns**
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Synthesized quantum circuit.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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**Raises**
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[**QiskitError**](exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if `pulse_optimize` is True but we don’t know how to do it.
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</Function>
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## Methods
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### decomp0
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.decomp0" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L556-L570" signature="decomp0(target)" modifiers="static">
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Decompose target $\sim U_d(x, y, z)$ with $0$ uses of the basis gate. Result $U_r$ has trace:
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$$
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\Big\vert\text{Tr}(U_r\cdot U_\text{target}^{\dag})\Big\vert =
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4\Big\vert (\cos(x)\cos(y)\cos(z)+ j \sin(x)\sin(y)\sin(z)\Big\vert
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$$
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which is optimal for all targets and bases
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</Function>
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### decomp1
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.decomp1" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L572-L584" signature="decomp1(target)">
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Decompose target $\sim U_d(x, y, z)$ with $1$ use of the basis gate $\sim U_d(a, b, c)$. Result $U_r$ has trace:
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$$
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\Big\vert\text{Tr}(U_r \cdot U_\text{target}^{\dag})\Big\vert =
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4\Big\vert \cos(x-a)\cos(y-b)\cos(z-c) + j \sin(x-a)\sin(y-b)\sin(z-c)\Big\vert
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$$
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which is optimal for all targets and bases with `z==0` or `c==0`.
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</Function>
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### decomp2\_supercontrolled
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.decomp2_supercontrolled" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L586-L603" signature="decomp2_supercontrolled(target)">
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Decompose target $\sim U_d(x, y, z)$ with $2$ uses of the basis gate.
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For supercontrolled basis $\sim U_d(\pi/4, b, 0)$, all b, result $U_r$ has trace
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$$
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\Big\vert\text{Tr}(U_r \cdot U_\text{target}^\dag) \Big\vert = 4\cos(z)
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$$
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which is the optimal approximation for basis of CNOT-class $\sim U_d(\pi/4, 0, 0)$ or DCNOT-class $\sim U_d(\pi/4, \pi/4, 0)$ and any target. It may be sub-optimal for $b \neq 0$ (i.e. there exists an exact decomposition for any target using $B \sim U_d(\pi/4, \pi/8, 0)$, but it may not be this decomposition). This is an exact decomposition for supercontrolled basis and target $\sim U_d(x, y, 0)$. No guarantees for non-supercontrolled basis.
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</Function>
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### decomp3\_supercontrolled
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.decomp3_supercontrolled" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L605-L611" signature="decomp3_supercontrolled(target)">
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Decompose target with $3$ uses of the basis. This is an exact decomposition for supercontrolled basis $\sim U_d(\pi/4, b, 0)$, all b, and any target. No guarantees for non-supercontrolled basis.
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</Function>
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### num\_basis\_gates
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.num_basis_gates" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L549-L554" signature="num_basis_gates(unitary)">
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Computes the number of basis gates needed in a decomposition of input unitary
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</Function>
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### traces
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<Function id="qiskit.synthesis.TwoQubitBasisDecomposer.traces" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/two_qubit/two_qubit_decompose.py#L694-L699" signature="traces(target)">
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Give the expected traces $\Big\vert\text{Tr}(U \cdot U_\text{target}^{\dag})\Big\vert$ for a different number of basis gates.
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</Function>
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</Class>
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