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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.

$$\begin{array}{r}\begin{array}{rl}|0⟩& \to |00\cdots 00⟩\\ |1⟩& \to \frac{|0\cdots 01⟩+|0\cdots 010⟩+|10\cdots 0⟩}{\sqrt{d-1}}\\ |2⟩& \to \frac{|0\cdots 011⟩+|0\cdots 0101⟩+|110\cdots 0⟩}{\sqrt{d-1}}\\ ⋮& ⋮\\ |d-1⟩& \to |11\cdots 11⟩\end{array}\end{array}$$

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]