g&fdZddlmZddlZddlmZddlmZddl m Z GddeZ dd Z dS)zHidden Linear Function circuit.) annotationsN)QuantumCircuit) CircuitError)deprecate_funccLeZdZdZedddd fd ZxZS) HiddenLinearFunctionaCircuit to solve the hidden linear function problem. 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 :math:`x_i`. The hidden linear function problem is as follows: Consider the quadratic form .. math:: q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4) and restrict :math:`q(x)` onto the nullspace of A. This results in a linear function. .. math:: 2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4) \forall x \in \mathrm{Ker}(A) and the goal is to recover this linear function (equivalently a vector :math:`[z_0, ..., z_{n-1}]`). There can be multiple solutions. 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 :math:`n`. Thus this circuit is an example of quantum advantage with shallow circuits. **Reference Circuit:** .. plot:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit.library import HiddenLinearFunction from qiskit.visualization.library import _generate_circuit_library_visualization A = [[1, 1, 0], [1, 0, 1], [0, 1, 1]] circuit = HiddenLinearFunction(A) _generate_circuit_library_visualization(circuit) **Reference:** [1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. `arXiv:1704.00690 `_ z1.3z:Use qiskit.circuit.library.hidden_linear_function instead.T)sinceadditional_msgpendingadjacency_matrixlist | np.ndarrayreturnNonect|}tj|jd|ji|||jdS)zCreate new HLF circuit. Args: adjacency_matrix: a symmetric n-by-n list of 0-1 lists. n will be the number of qubits. Raises: CircuitError: If A is not symmetric. nameN)hidden_linear_functionsuper__init__qregsrappendto_gatequbits)selfr circuit __class__s c/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/hidden_linear_function.pyrzHiddenLinearFunction.__init__HsY))9::'-;gl;;; GOO%%t{33333)r r rr)__name__ __module__ __qualname____doc__rr __classcell__)rs@rrrsq..`^S 4 4 4 4 4  4 4 4 4 4rrr r rrcjtj|}tj||st dt |}t |d|}|t|t|D]<}t|dz|D]&}|||r| ||'=t|D]%}|||r| |&|t||S)aCircuit to solve the hidden linear function problem. 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 :math:`x_i`. The hidden linear function problem is as follows: Consider the quadratic form .. math:: q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4) and restrict :math:`q(x)` onto the nullspace of A. This results in a linear function. .. math:: 2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4) \forall x \in \mathrm{Ker}(A) and the goal is to recover this linear function (equivalently a vector :math:`[z_0, ..., z_{n-1}]`). There can be multiple solutions. 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 :math:`n`. Thus this circuit is an example of quantum advantage with shallow circuits. **Reference Circuit:** .. plot:: :alt: Circuit diagram output by the previous code. :include-source: from qiskit.circuit.library import hidden_linear_function A = [[1, 1, 0], [1, 0, 1], [0, 1, 1]] circuit = hidden_linear_function(A) circuit.draw('mpl') Args: adjacency_matrix: a symmetric n-by-n list of 0-1 lists. n will be the number of qubits. Raises: CircuitError: If A is not symmetric. **Reference:** [1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. `arXiv:1704.00690 `_ z'The adjacency matrix must be symmetric.zhlf: )r) npasarrayallclose transposerlenrhrangeczs)r num_qubitsrijs rrr\sFnz"233 ;')9)C)C)E)E F FFDEEE%&&JZ.H6F.H.HIIIG IIeJ   :  !!q1uj)) ! !A"1% ! 1a    !:   A q !  IIaLLL IIeJ   Nr)r r rr) r! __future__rnumpyr%qiskit.circuit.quantumcircuitrqiskit.circuit.exceptionsrqiskit.utils.deprecationrrrrrr7s&%""""""888888222222333333B4B4B4B4B4>B4B4B4JGGGGGGr