z i`SrSSKJr SSKrSSKJr SSKJr SSK J r "SS\5r S S jr g) zHidden Linear Function circuit.) annotationsN)QuantumCircuit) CircuitError)deprecate_funccF^\rSrSrSr\"SSSS9S U4Sjj5rSrU=r$) HiddenLinearFunctiona&Circuit 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) References: [1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. `arXiv:1704.00690 `_ z2.1z:Use qiskit.circuit.library.hidden_linear_function instead.z in Qiskit 3.0)sinceadditional_msgremoval_timelinec>[U5n[TU]"URSUR06 UR UR 5UR5 g)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)selfadjacency_matrixcircuit __class__s g/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/hidden_linear_function.pyrHiddenLinearFunction.__init__HsC))9: '--;gll; GOO%t{{3)rlist | np.ndarrayreturnNone) __name__ __module__ __qualname____firstlineno____doc__rr__static_attributes__ __classcell__)rs@rrrs+.`S( 4  4rrc"[R"U5n[R"XR55(d [ S5e[ U5n[ USU3S9nUR[U55 [U5H8n[US-U5H"nXU(dMURX45 M$ M: [U5H"nXU(dMURU5 M$ UR[U55 U$)aYCircuit 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\snzz"23 ;;')C)C)E F FDEE%&JZ6F5G.HIG IIeJ : q1uj)A"1%% 1 *:   q ! ! IIaL IIeJ Nr)rrrr) r% __future__rnumpyr*qiskit.circuit.quantumcircuitrqiskit.circuit.exceptionsrqiskit.utils.deprecationrrrrrrr;s.&"823B4>B4JGr