52 lines
2.6 KiB
Plaintext
52 lines
2.6 KiB
Plaintext
---
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title: fourier_checking (latest version)
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description: API reference for qiskit.circuit.library.fourier_checking 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.fourier_checking
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---
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<span id="fourier-checking" />
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# fourier\_checking
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<Class id="qiskit.circuit.library.fourier_checking" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/fourier_checking.py#L104-L160" signature="qiskit.circuit.library.fourier_checking(f, g)" modifiers="class">
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Bases:
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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 Circuit:**
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```python
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from qiskit.circuit.library import fourier_checking
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circuit = fourier_checking([1, -1, -1, -1], [1, 1, -1, -1])
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circuit.draw('mpl')
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```
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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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**Parameters**
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* **f** ([*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*]*) –
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* **g** ([*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.13)")*\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")*]*) –
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**Return type**
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[*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")
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</Class>
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