Apply a single‑qubit Pauli noise channel independently to each of `n` qubits. For every qubit the channel does: 0 → I with pro

apply a random rotation to each qubit

Smoothly normalize a real input value to the interval (-1, 1) using 'sigmoid' with steepness parameter k.

Reconstruct the odd part of an ``R``-frequency input function via equidistant shifts.

Implements the ordered statistics decoding with order-0 fallback

Computes the squared overlap between Chebyshev states.

Helper function to convert a string to a list of Pandoc Str nodes.

Parse the body of an intersphinx link.

Calculates the expectation value of the operator with the IQP circuit with PennyLane tools. Args: params (np.ndarray): The parameters of

Returns a PennyLane observable from a bitstring representation. Args: op (np.ndarray): Bitstring representation of the Z operator. R

Ansatz to embed a graph with node and edge weights into a quantum state. The adjacency matrix A contains the edge weights on the off-dia

Reorders amplitudes of the conditioned states.

Play episodes in parallel.

Plot the rotation axes in the Bloch sphere.

Calculate polynomial degree parameters from Zhou et al. (2025)

Adds a pooling layer to a circuit. Args: weights (np.array): Array with the weights of the conditional U3 gate. wires (list[int]):

Prepares the |H> magic state on wire 1.

Process a doc/demo link.

Process the header cells of a table. Return a list of text strings for each header cell.

Process the rows of a table. Return a list of lists of text strings for each cell in each row.

Compute the fidelity function for given parameters.

Returns the normalization constant <psi|psi>, where |psi> = A |x>.

Push an operator from left to right along the bond sites of an MPS and conditionally apply correcting operations on the corresponding physical sit

Prepare a state \sum_x f(x) |x> and apply the discrete Fourier transform.

Prepare a state \sum_x f(x) |x> and apply the Fourier transform over Z_2^4.

Generate a Haar-random matrix using the QR decomposition.

A variational quantum model.

Predict using the quantum model defined above.

Train the quantum model defined above.

The variational quantum circuit.

Create a random observable on N qubits.

Generate random variational parameters in the shape for the ansatz.

Create a random state on N qubits.

Estimates the parameter gradient from the episodes with a state-independent baseline.

Build the (n − 1) × n parity‑check matrix H for the [n, 1] repetition code. Each row enforces equality between two neighboring bits:

Rotates and shifts the phase of the auxiliary qubit and rotates the jth qubit by pi/2^(j+1) in Z.

Given a fixed value 'a', compute the signal rotation matrix W(a). (requires -1 <= 'a' <= 1)