fix unicode

Author: WeiguoMa

tensorcircuit/applications/layers.py

@@ -35,7 +35,7 @@
 
 def _resolve(symbol: Union[Symbol, Tensor], i: int = 0) -> Tensor:
     """
-    Make sure the layer is compatible with both multi-param and single param requirements。
+    Make sure the layer is compatible with both multi-param and single param requirements
 
     What could be the input: list/tuple of sympy.symbol, tf.tensor with 1D or 0D shape
     """

tensorcircuit/backends/abstract_backend.py

@@ -1039,8 +1039,8 @@ def searchsorted(self: Any, a: Tensor, v: Tensor, side: str = "left") -> Tensor:
         :type a: Tensor
         :param v: value to inserted
         :type v: Tensor
-        :param side:  If ‘left’, the index of the first suitable location found is given.
-            If ‘right’, return the last such index.
+        :param side:  If `left`, the index of the first suitable location found is given.
+            If `right`, return the last such index.
             If there is no suitable index, return either 0 or N (where N is the length of a),
             defaults to "left"
         :type side: str, optional

tensorcircuit/densitymatrix.py

@@ -179,9 +179,9 @@ def _contract(self) -> None:
 
     @staticmethod
     def check_kraus(kraus: Sequence[Gate]) -> bool:
-        """
+        r"""
         Check if Kraus operators satisfy the completeness relation:
-        sum_i K_i^† K_i = I
+        :math:`\sum_i K_i^\dagger K_i = I`
 
         :param kraus: Sequence of Kraus operators
         :type kraus: Sequence[Gate]

tensorcircuit/quantum.py

@@ -79,7 +79,7 @@ def _decode_basis_label(label: str, n: int, dim: int) -> List[int]:
     """
     Decode a string basis label into a list of integer digits.
 
-    The label is interpreted in base-``dim`` using characters ``0–9A–Z``.
+    The label is interpreted in base-``dim`` using characters ``0-9A-Z``.
     Only dimensions up to 36 are supported.
 
     :param label: basis label string, e.g. "010" or "A9F"
@@ -97,7 +97,7 @@ def _decode_basis_label(label: str, n: int, dim: int) -> List[int]:
     """
     if dim > 36:
         raise NotImplementedError(
-            f"String basis label supports d<=36 (0–9A–Z). Got dim={dim}. "
+            f"String basis label supports d<=36 (0-9A-Z). Got dim={dim}. "
             "Use an integer array/tensor of length n instead."
         )
     s = label.upper()
@@ -107,7 +107,7 @@ def _decode_basis_label(label: str, n: int, dim: int) -> List[int]:
     for ch in s:
         if ch not in _ALPHABET:
             raise ValueError(
-                f"Invalid character '{ch}' in basis label (allowed 0–9A–Z)."
+                f"Invalid character '{ch}' in basis label (allowed 0-9A-Z)."
             )
         v = _ALPHABET.index(ch)
         if v >= dim:
@@ -751,7 +751,7 @@ def tensor_product(self, other: "QuOperator") -> "QuOperator":
         """
         Tensor product with another operator.
         Given two operators `A` and `B`, produces a new operator `AB` representing
-        :math:`A ⊗ B`. The `out_edges` (`in_edges`) of `AB` is simply the
+        :math:`A \otimes B`. The `out_edges` (`in_edges`) of `AB` is simply the
         concatenation of the `out_edges` (`in_edges`) of `A.copy()` with that of
         `B.copy()`:
         `new_out_edges = [*out_edges_A_copy, *out_edges_B_copy]`
@@ -2403,13 +2403,13 @@ def free_energy(
 
 def renyi_entropy(rho: Union[Tensor, QuOperator], k: int = 2) -> Tensor:
     """
-    Compute the Rényi entropy of order :math:`k` by given density matrix.
+    Compute the Renyi entropy of order :math:`k` by given density matrix.
 
     :param rho: The density matrix in form of Tensor or QuOperator.
     :type rho: Union[Tensor, QuOperator]
-    :param k: The order of Rényi entropy, default is 2.
+    :param k: The order of Renyi entropy, default is 2.
     :type k: int, optional
-    :return: The :math:`k` th order of Rényi entropy.
+    :return: The :math:`k` th order of Renyi entropy.
     :rtype: Tensor
     """
     s = 1 / (1 - k) * backend.real(backend.log(trace_product(*[rho for _ in range(k)])))
@@ -2423,7 +2423,7 @@ def renyi_free_energy(
     k: int = 2,
 ) -> Tensor:
     """
-    Compute the Rényi free energy of the corresponding density matrix and Hamiltonian.
+    Compute the Renyi free energy of the corresponding density matrix and Hamiltonian.
 
     :Example:
 
@@ -2440,9 +2440,9 @@ def renyi_free_energy(
     :type h: Union[Tensor, QuOperator]
     :param beta: Constant for the optimization, default is 1.
     :type beta: float, optional
-    :param k: The order of Rényi entropy, default is 2.
+    :param k: The order of Renyi entropy, default is 2.
     :type k: int, optional
-    :return: The :math:`k` th order of Rényi entropy.
+    :return: The :math:`k` th order of Renyi entropy.
     :rtype: Tensor
     """
     energy = backend.real(trace_product(rho, h))

tensorcircuit/results/counts.py

@@ -140,7 +140,7 @@ def count2vec(
 def vec2count(vec: Tensor, prune: bool = False, dim: Optional[int] = None) -> ct:
     """
     Map a count/probability vector of length D to a dictionary with base-d string keys (0-9A-Z).
-    Only generate string keys when d ≤ 36; if d is inferred to be > 36, raise a NotImplementedError.
+    Only generate string keys when d <= 36; if d is inferred to be > 36, raise a NotImplementedError.
 
     :param vec: A one-dimensional vector of length D = d**n
     :param prune: Whether to prune near-zero elements (threshold 1e-8)

tensorcircuit/shadows.py

@@ -334,7 +334,7 @@ def entropy_shadow(
 
 def renyi_entropy_2(snapshots: Tensor, sub: Optional[Sequence[int]] = None) -> Tensor:
     r"""To calculate the second order Renyi entropy of a subsystem from snapshot, please refer to
-    Brydges, T. et al. Science 364, 260–263 (2019). This function is not jitable.
+    Brydges, T. et al. Science 364, 260-263 (2019). This function is not jitable.
 
     :param snapshots: shape = (ns, repeat, nq)
     :type: Tensor

tensorcircuit/templates/hamiltonians.py

@@ -19,11 +19,11 @@ def heisenberg_hamiltonian(
     j_coupling: Union[float, List[float], Tuple[float, ...]] = 1.0,
     interaction_scope: str = "neighbors",
 ) -> Any:
-    """
+    r"""
     Generates the sparse matrix of the Heisenberg Hamiltonian for a given lattice.
 
     The Heisenberg Hamiltonian is defined as:
-    H = J * Σ_{i,j} (X_i X_j + Y_i Y_j + Z_i Z_j)
+    :math:`H = J\sum_{i,j} (X_i X_j + Y_i Y_j + Z_i Z_j)`
     where the sum is over a specified set of interacting pairs {i,j}.
 
     :param lattice: An instance of a class derived from AbstractLattice,
@@ -86,13 +86,21 @@ def heisenberg_hamiltonian(
 def rydberg_hamiltonian(
     lattice: AbstractLattice, omega: float, delta: float, c6: float
 ) -> Any:
-    """
+    r"""
     Generates the sparse matrix of the Rydberg atom array Hamiltonian.
 
     The Hamiltonian is defined as:
-    H = Σ_i (Ω/2)X_i - Σ_i δ(1 - Z_i)/2 + Σ_{i<j} V_ij (1-Z_i)/2 (1-Z_j)/2
-      = Σ_i (Ω/2)X_i + Σ_i (δ/2)Z_i + Σ_{i<j} (V_ij/4)(Z_iZ_j - Z_i - Z_j)
-    where V_ij = C6 / |r_i - r_j|^6.
+    .. math::
+
+    H = \sum_i \frac{\Omega}{2} X_i
+        - \sum_i \frac{\delta}{2} \bigl(1 - Z_i \bigr)
+        + \sum_{i<j} \frac{V_{ij}}{4} \bigl(1 - Z_i \bigr)\bigl(1 - Z_j \bigr)
+
+      = \sum_i \frac{\Omega}{2} X_i
+        + \sum_i \frac{\delta}{2} Z_i
+        + \sum_{i<j} \frac{V_{ij}}{4}\,\bigl(Z_i Z_j - Z_i - Z_j \bigr)
+
+    where :math:`V_{ij} = C6 / |r_i - r_j|^6`.
 
     Note: Constant energy offset terms (proportional to the identity operator)
     are ignored in this implementation.

tensorcircuit/templates/lattice.py

@@ -1436,7 +1436,7 @@ def _build_neighbors(self, max_k: int = 1, **kwargs: Any) -> None:
         This method supports two modes:
         1. KDTree mode (use_kdtree=True): Fast, O(N log N) performance for large lattices
            but breaks differentiability due to scipy dependency
-        2. Distance matrix mode (use_kdtree=False): Slower O(N²) but fully differentiable
+        2. Distance matrix mode (use_kdtree=False): Slower O(N^2) but fully differentiable
            and backend-agnostic
 
         :param max_k: Maximum number of neighbor shells to compute

tensorcircuit/timeevol.py

@@ -387,7 +387,7 @@ def hamiltonian_evol(
     ...     [0.0, 2.0, -1.0, 0.0],
     ...     [0.0, 0.0, 0.0, 1.0]
     ... ])
-    >>> # Initial state |00⟩
+    >>> # Initial state |00>
     >>> psi0 = tc.array_to_tensor([1.0, 0.0, 0.0, 0.0])
     >>> # Evolution times
     >>> times = tc.array_to_tensor([0.0, 0.5, 1.0])
@@ -843,7 +843,7 @@ def estimate_spectral_bounds(
     :type n_iter: int
     :param psi0: Optional initial state.
     :type psi0: Optional[Any]
-    :return: (E_max, E_min)。
+    :return: (E_max, E_min)
     """
     shape = h.shape
     D = shape[-1]