mindquantum.algorithm.library.qudit_symmetric_encoding

mindquantum.algorithm.library.qudit_symmetric_encoding(qudit: np.ndarray, n_qudits: int = 1, is_csr: bool = False)

Qudit symmetric encoding, encodes a qudit state or matrix into a qubit symmetric state or matrix.

\[\begin{split}\begin{align} \ket{0}&\to\ket{00\cdots00} \\[.5ex] \ket{1}&\to\frac{\ket{0\cdots01}+\ket{0\cdots010}+\ket{10\cdots0}}{\sqrt{d-1}} \\ \ket{2}&\to\frac{\ket{0\cdots011}+\ket{0\cdots0101}+\ket{110\cdots0}}{\sqrt{d-1}} \\ \vdots&\qquad\vdots \\[.5ex] \ket{d-1}&\to\ket{11\cdots11} \end{align}\end{split}\]

Parameters

• qudit (np.ndarray) – the qudit state or matrix that needs to be encoded.

• n_qudits (int) – the number of qudits in the qudit state or matrix. Default: 1.

• is_csr (bool) – whether to return the matrix in CSR (Compressed Sparse Row) format. Default: False.

Returns

np.ndarray, the qubit symmetric state or matrix obtained after the qudit symmetric encoding.

Examples

>>> import numpy as np
>>> from mindquantum.algorithm.library.qudit_mapping import qudit_symmetric_encoding
>>> qudit = np.array([1., 2., 3.])
>>> qudit /= np.linalg.norm(qudit)
>>> print(qudit)
[0.26726124 0.53452248 0.80178373]
>>> print(qudit_symmetric_encoding(qudit))
[0.26726124+0.j 0.37796447+0.j 0.37796447+0.j 0.80178373+0.j]