280 lines
12 KiB
Plaintext
280 lines
12 KiB
Plaintext
---
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title: FourierChecking (v1.2)
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description: API reference for qiskit.circuit.library.FourierChecking 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.circuit.library.FourierChecking
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---
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# FourierChecking
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<Class id="qiskit.circuit.library.FourierChecking" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/fourier_checking.py#L24-L97" signature="qiskit.circuit.library.FourierChecking(f, g)" modifiers="class">
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Bases: [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")
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Fourier checking circuit.
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The circuit for the Fourier checking algorithm, introduced in \[1], involves a layer of Hadamards, the function $f$, another layer of Hadamards, the function $g$, followed by a final layer of Hadamards. The functions $f$ and $g$ are classical functions realized as phase oracles (diagonal operators with \{-1, 1} on the diagonal).
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The probability of observing the all-zeros string is $p(f,g)$. The algorithm solves the promise Fourier checking problem, which decides if f is correlated with the Fourier transform of g, by testing if $p(f,g) <= 0.01$ or $p(f,g) >= 0.05$, promised that one or the other of these is true.
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The functions $f$ and $g$ are currently implemented from their truth tables but could be represented concisely and implemented efficiently for special classes of functions.
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Fourier checking is a special case of $k$-fold forrelation \[2].
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**Reference:**
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\[1] S. Aaronson, BQP and the Polynomial Hierarchy, 2009 (Section 3.2). [arXiv:0910.4698](https://arxiv.org/abs/0910.4698)
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\[2] S. Aaronson, A. Ambainis, Forrelation: a problem that optimally separates quantum from classical computing, 2014. [arXiv:1411.5729](https://arxiv.org/abs/1411.5729)
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Create Fourier checking circuit.
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**Parameters**
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* **f** ([*List*](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*]*) – truth table for f, length 2\*\*n list of \{1,-1}.
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* **g** ([*List*](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*]*) – truth table for g, length 2\*\*n list of \{1,-1}.
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**Raises**
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[**CircuitError**](circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – if the inputs f and g are not valid.
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**Reference Circuit:**
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.FourierChecking.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.FourierChecking.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.FourierChecking.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.FourierChecking.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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### global\_phase
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<Attribute id="qiskit.circuit.library.FourierChecking.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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### instances
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<Attribute id="qiskit.circuit.library.FourierChecking.instances" attributeValue="168" />
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### layout
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<Attribute id="qiskit.circuit.library.FourierChecking.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.FourierChecking.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.FourierChecking.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.FourierChecking.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.FourierChecking.num_input_vars "qiskit.circuit.library.FourierChecking.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.FourierChecking.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.FourierChecking.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.FourierChecking.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.FourierChecking.num_captured_vars "qiskit.circuit.library.FourierChecking.num_captured_vars") must be zero.
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.FourierChecking.num_parameters">
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The number of parameter objects in the circuit.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.FourierChecking.num_qubits">
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Return number of qubits.
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</Attribute>
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### num\_vars
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<Attribute id="qiskit.circuit.library.FourierChecking.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.FourierChecking.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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### parameters
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<Attribute id="qiskit.circuit.library.FourierChecking.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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### prefix
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<Attribute id="qiskit.circuit.library.FourierChecking.prefix" attributeValue="'circuit'" />
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### qubits
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<Attribute id="qiskit.circuit.library.FourierChecking.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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### name
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<Attribute id="qiskit.circuit.library.FourierChecking.name" attributeTypeHint="str">
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A human-readable name for the circuit.
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</Attribute>
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### qregs
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<Attribute id="qiskit.circuit.library.FourierChecking.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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### cregs
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<Attribute id="qiskit.circuit.library.FourierChecking.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.FourierChecking.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.FourierChecking.unit "qiskit.circuit.library.FourierChecking.unit").
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.FourierChecking.unit">
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The unit that [`duration`](#qiskit.circuit.library.FourierChecking.duration "qiskit.circuit.library.FourierChecking.duration") is specified in.
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</Attribute>
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</Class>
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