Sample random states from the Haar measure.

Just sorting the outputs in a dictionary

Calculate the shadow bound for the Pauli measurement scheme. Implements Eq. (S13) from https://arxiv.org/pdf/2002.08953.pdf Args:

Reconstruct a state approximation as an average over all snapshots in the shadow. Args: shadow (tuple): A shadow tuple obtained from

Sigmoid function with steepness parameter k.

Smooth-rectangle pulse between t_0 and t_1, with amplitude Omega.

Split a matrix M via SVD and keep only the ``bond_dim`` largest entries.

Kernel-target alignment between kernel and labels.

Computes the state amplitudes of tau in the computational basis.

Given the anomaly scores and truth values, scan over a range of thresholds = [zeta_min, zeta_max] with a fixed number of steps, calculating th

Single optimization step in the training procedure.

Perform a single gradient update step

Perform a single gradient update step

Variational circuit mapping the ground state |0> to the ansatz state |x>.

Variational circuit mapping the ground state |0> to the ansatz state |x>.

Compute the tensor A in form of d=2 matrices with shape (D, D) = (2, 2) each.

Controlled application of all the unitary components A_l of the problem matrix A.

Apply a controlled RX on all wires in a ring pattern

Generates an n_qubit quantum circuit according to a k-local Walsh operator expansion. Here, k-local means that 1 <= k <= n of the n qubits can int

Quantum circuit implementing the DQI algorithm to solve max-XORSAT.

Layer of single-qubit Hadamard gates.

Create a docplex model of the problem. (Docplex is a classical solver from IBM)

Defines the unitary that implements a function f:{0,..,15} -> {0,..,7}. Args: f (func): function to implement Returns: ndar

Unitary matrix rotating the system ground state to the problem vector |b> = U_b |0>.

Unitary matrix rotating the ground state of the ancillary qubits to |sqrt(c)> = U_c |0>.

Adjoint of U_c.

Circuit implementing the Z rotations of the Hamiltonian fragments.

Parametrized quantum circuit ansatz that alternates arbitrary single-qubit rotations with strongly entangling CNOT layers. The depth of the ansatz

Compute the next round of check‑to‑variable messages.

Collect author information from user input.

Create demo.py and metadata.json files.

Parse the error section from sphinx-gallery output. Returns `None` if the error section could not be found.

Initialize a virtual environment.