66 lines
2.6 KiB
Plaintext
66 lines
2.6 KiB
Plaintext
---
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title: hidden_linear_function (latest version)
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description: API reference for qiskit.circuit.library.hidden_linear_function 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.hidden_linear_function
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---
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<span id="hidden-linear-function" />
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# hidden\_linear\_function
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<Class id="qiskit.circuit.library.hidden_linear_function" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/hidden_linear_function.py#L92-L163" signature="qiskit.circuit.library.hidden_linear_function(adjacency_matrix)" modifiers="class">
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Bases:
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Circuit to solve the hidden linear function problem.
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The 2D Hidden Linear Function problem is determined by a 2D adjacency matrix A, where only elements that are nearest-neighbor on a grid have non-zero entries. Each row/column corresponds to one binary variable $x_i$.
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The hidden linear function problem is as follows:
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Consider the quadratic form
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$$
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q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4)
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$$
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and restrict $q(x)$ onto the nullspace of A. This results in a linear function.
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$$
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2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4) \forall x \in \mathrm{Ker}(A)
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$$
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and the goal is to recover this linear function (equivalently a vector $[z_0, ..., z_{n-1}]$). There can be multiple solutions.
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In \[1] it is shown that the present circuit solves this problem on a quantum computer in constant depth, whereas any corresponding solution on a classical computer would require circuits that grow logarithmically with $n$. Thus this circuit is an example of quantum advantage with shallow circuits.
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**Reference Circuit:**
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```python
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from qiskit.circuit.library import hidden_linear_function
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A = [[1, 1, 0], [1, 0, 1], [0, 1, 1]]
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circuit = hidden_linear_function(A)
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circuit.draw('mpl')
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```
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**Parameters**
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**adjacency\_matrix** ([*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.13)") *| np.ndarray*) – a symmetric n-by-n list of 0-1 lists. n will be the number of qubits.
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**Raises**
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[**CircuitError**](circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If A is not symmetric.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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**Reference:**
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\[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. [arXiv:1704.00690](https://arxiv.org/abs/1704.00690)
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</Class>
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