adjust some unicode and doc fixing.

Author: WeiguoMa

examples/time_evolution_comparison.py

@@ -27,7 +27,11 @@ def create_heisenberg_hamiltonian(n, sparse=True):
 
 
 def create_initial_state(n):
-    """Create initial Neel state |↑↓↑↓↑↓↑↓> for n sites."""
+    r"""
+    Create initial Neel state
+    :math:`\vert \uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\rangle`
+    for n sites.
+    """
     c = tc.Circuit(n)
     # Apply X gates to odd sites to create Neel state
     c.x([i for i in range(1, n, 2)])

examples/vqe_qudit_example.py

@@ -4,7 +4,7 @@
 This example shows how to run a simple VQE on a qudit system using
 `tensorcircuit.QuditCircuit`. We build a compact ansatz using single-qudit
 rotations in selected two-level subspaces and RXX-type entanglers, then
-optimize the energy of a Hermitian "clock–shift" Hamiltonian:
+optimize the energy of a Hermitian "clock-shift" Hamiltonian:
 
     H(d) = - J * (X_c \otimes X_c)  -  h * (Z_c \otimes I + I \otimes Z_c)
 
@@ -31,12 +31,12 @@
 
 
 def vqe_forward(param, *, nqudits: int, d: int, nlayers: int, J: float, h: float):
-    """Build a QuditCircuit ansatz and compute ⟨H⟩.
+    r"""Build a QuditCircuit ansatz and compute :math:`\langle H\rangle`.
 
     Ansatz:
       [ for L in 1...nlayers ]
         - On each site q:
-            RX(q; θ_Lq^(01)) ∘ RY(q; θ_Lq^(12)) ∘ RZ(q; φ_Lq^(0))
+            :math:`RX(q; \theta_L q^(01)) RY(q; \theta_L q^(12)) RZ(q; \phi_L q^(0))`
           (subspace indices shown as superscripts)
         - Entangle neighboring pairs with RXX on subspaces (0,1)
     """
@@ -86,7 +86,7 @@ def build_param_shape(nqudits: int, d: int, nlayers: int):
 
 def main():
     parser = argparse.ArgumentParser(
-        description="VQE on QuditCircuit (clock–shift model)"
+        description="VQE on QuditCircuit (clock-shift model)"
     )
     parser.add_argument(
         "--d", type=int, default=3, help="Local dimension per site (>=3)"

tensorcircuit/basecircuit.py

@@ -3,7 +3,7 @@
 
 Note:
   - Supports qubit (d = 2) and qudit (d >= 2) systems.
-  - For string-encoded samples/counts when d <= 36, digits use base-d characters 0–9A–Z (A = 10, …, Z = 35).
+  - For string-encoded samples/counts when d <= 36, digits use base-d characters 0-9A-Z (A = 10, ..., Z = 35).
 """
 
 # pylint: disable=invalid-name
@@ -362,7 +362,7 @@ def to_qir(self) -> List[Dict[str, Any]]:
 
     def perfect_sampling(self, status: Optional[Tensor] = None) -> Tuple[str, float]:
         """
-        Sampling base-d strings (0–9A–Z when d <= 36) from the circuit output based on quantum amplitudes.
+        Sampling base-d strings (0-9A-Z when d <= 36) from the circuit output based on quantum amplitudes.
         Reference: arXiv:1201.3974.
 
         :param status: external randomness, with shape [nqubits], defaults to None
@@ -604,7 +604,7 @@ def sample(
                 "count_tuple": # (np.array([0]), np.array([2]))
 
                 "count_dict_bin": # {"00": 2, "01": 0, "10": 0, "11": 0}
-                    for cases d\in [11, 36], use 0–9A–Z digits (e.g., 'A' -> 10, …, 'Z' -> 35);
+                    for cases d\in [11, 36], use 0-9A-Z digits (e.g., 'A' -> 10, ..., 'Z' -> 35);
 
                 "count_dict_int": # {0: 2, 1: 0, 2: 0, 3: 0}
 

tensorcircuit/circuit.py

@@ -1,7 +1,7 @@
 """
 Quantum circuit: the state simulator.
 Supports qubit (dim=2) and qudit (3 <= dim <= 36) systems.
-For string-encoded samples/counts, digits use 0–9A–Z where A=10, …, Z=35.
+For string-encoded samples/counts, digits use 0-9A-Z where A=10, ..., Z=35.
 """
 
 # pylint: disable=invalid-name
@@ -768,7 +768,7 @@ def measure_reference(
         Take measurement on the given quantum lines by ``index``.
 
         Return format:
-        - For d <= 36, the sample is a base-d string using 0–9A–Z (A=10,…).
+        - For d <= 36, the sample is a base-d string using 0-9A-Z (A=10,...).
 
         :Example:
 

tensorcircuit/quditcircuit.py

@@ -3,7 +3,7 @@
 
 This module provides a high-level `QuditCircuit` API that mirrors `tensorcircuit.circuit.Circuit`
 but targets qudits with dimension `3 <= d <= 36`.
-For string-encoded samples/counts, digits use `0–9A–Z` where `A=10, …, Z=35`.
+For string-encoded samples/counts, digits use `0-9A-Z` where `A=10, ..., Z=35`.
 
 .. note::
    For qubits (`d=2`) please use :class:`tensorcircuit.circuit.Circuit`.
@@ -42,8 +42,8 @@ class QuditCircuit:
     >>> c.sample(1024, format="count_dict_bin")
 
     .. note::
-       For `3 <= d <= 36`, string samples and count keys use base-`d` characters `0–9A–Z`
-       (`A=10, …, Z=35`).
+       For `3 <= d <= 36`, string samples and count keys use base-`d` characters `0-9A-Z`
+       (`A=10, ..., Z=35`).
 
     :param nqudits: Number of qudits (wires) in the circuit.
     :type nqudits: int
@@ -94,7 +94,7 @@ def _set_dim(self, dim: int) -> None:
                 f"QuditCircuit is only for qudits (dim>=3). "
                 f"You passed dim={dim}. For qudits, please use `Circuit` instead."
             )
-        # Require integer d>=2; current string-encoded IO supports d<=36 (0–9A–Z digits).
+        # Require integer d>=2; current string-encoded IO supports d<=36 (0-9A-Z digits).
         if dim > 36:
             raise NotImplementedError(
                 "The Qudit interface is only supported for dimension < 36 now."
@@ -486,7 +486,7 @@ def amplitude(self, l: Union[str, Tensor]) -> Tensor:
         >>> c.amplitude("21")
         array(1.+0.j, dtype=complex64)
 
-        :param l: Bitstring in base-`d` using `0–9A–Z`.
+        :param l: Bitstring in base-`d` using `0-9A-Z`.
         :type l: Union[str, Tensor]
         :return: Complex amplitude.
         :rtype: Tensor
@@ -528,7 +528,7 @@ def sample(
                 "count_vector": # np.array([2, 0, 0, 0])
 
                 "count_dict_bin": # {"00": 2, "01": 0, "10": 0, "11": 0}
-                    for cases d\in [11, 36], use 0–9A–Z digits (e.g., 'A' -> 10, …, 'Z' -> 35);
+                    for cases :math:`d\in [11, 36]`, use 0-9A-Z digits (e.g., 'A' -> 10, ..., 'Z' -> 35);
 
         :type format: Optional[str]
         :param random_generator: random generator,  defaults to None
@@ -593,7 +593,7 @@ def mid_measurement(self, index: int, keep: int = 0) -> Tensor:
 
         :param index: Qudit index where post-selection is applied.
         :type index: int
-        :param keep: Post-selected digit in `{0, …, d-1}`.
+        :param keep: Post-selected digit in `{0, ..., d-1}`.
         :type keep: int
         :return: Unnormalized post-selected state.
         :rtype: Tensor
@@ -662,7 +662,7 @@ def amplitude_before(self, l: Union[str, Tensor]) -> List[Gate]:
         For density-matrix simulators,
         it would correspond to :math:`\operatorname{Tr}(\rho \vert l \rangle \langle l \vert)`.
 
-        :param l: Base-`d` string using `0–9A–Z` or an equivalent tensor index.
+        :param l: Base-`d` string using `0-9A-Z` or an equivalent tensor index.
         :type l: Union[str, Tensor]
         :return: The tensornetwork nodes for the amplitude of the circuit.
         :rtype: List[Gate]

tensorcircuit/quditgates.py

@@ -195,7 +195,7 @@ def _check_rotation_indices(
         j1, k1, j2, k2 = indices
         if j1 == k1 and j2 == k2:
             raise ValueError(
-                "Selected basis states must be different: (j1, j2) ≠ (k1, k2)."
+                "Selected basis states must be different: (j1, j2) != (k1, k2)."
             )
 
 
@@ -343,7 +343,7 @@ def rzz_matrix_func(
     Two-qudit ``RZZ(\theta)`` on a selected two-state subspace.
 
     Acts like a qubit :math:`RZZ(\theta)=\exp(-i\,\tfrac{\theta}{2}\,\sigma_z)` on the
-    two-dimensional subspace spanned by ``|j1, j2⟩`` and ``|k1, k2⟩``,
+    two-dimensional subspace spanned by :math:`\lvert j1, j2\rangle` and :math:`\lvert k1, k2\rangle`,
     and as identity elsewhere. The resulting block is diagonal with phases
     :math:`\mathrm{diag}(e^{-i\theta/2},\, e^{+i\theta/2})`.
 
@@ -384,7 +384,8 @@ def rxx_matrix_func(
     r"""
     Two-qudit ``RXX(\theta)`` on a selected two-state subspace.
 
-    Acts like a qubit :math:`RXX` on the subspace spanned by ``|j1, j2⟩`` and ``|k1, k2⟩``.
+    Acts like a qubit :math:`RXX` on the subspace spanned by
+    :math:`\lvert j1, j2\rangle` and :math:`\lvert k1, k2\rangle`.
 
     :param d: Dimension of each qudit (assumed equal).
     :type d: int
@@ -429,7 +430,7 @@ def u8_matrix_func(
     ``U8`` diagonal single-qudit gate for prime dimensions.
 
     See ref: Howard, Mark, and Jiri Vala.
-    "Qudit versions of the qubit π/8 gate." Physical Review A 86, no. 2 (2012): 022316.
+    "Qudit versions of the qubit \pi/8 gate." Physical Review A 86, no. 2 (2012): 022316.
     https://doi.org/10.1103/PhysRevA.86.022316
 
     This gate is the qudit analogue of the qubit :math:`\pi/8` gate, defined in
@@ -448,8 +449,8 @@ def u8_matrix_func(
     :param d: Qudit dimension (must be prime).
     :type d: int
     :param gamma: Shear parameter :math:`\gamma' \in \mathbb{Z}_d`.
-        If ``gamma = 0``, the gate is a diagonal Clifford.
-        If ``gamma ≠ 0``, the gate is a genuine non-Clifford (analogue of :math:`\pi/8`).
+        If :math:`gamma = 0`, the gate is a diagonal Clifford.
+        If :math:`gamma \neq 0`, the gate is a genuine non-Clifford (analogue of :math:`\pi/8`).
     :type gamma: int
     :param z: Displacement parameter :math:`z' \in \mathbb{Z}_d`,
         which sets the symplectic part of the associated Clifford.

tests/test_quditcircuit.py

@@ -350,8 +350,8 @@ def test_quditcircuit_set_dim_validation():
 
 @pytest.mark.parametrize("backend", [lf("jaxb"), lf("tfb"), lf("torchb")])
 def test_qudit_minimal_ad_qudit(backend):
-    """Minimal AD test on a single-qudit (d=3) circuit.
-    We differentiate the expectation ⟨Z⟩ w.r.t. a single RY parameter and
+    r"""Minimal AD test on a single-qudit (d=3) circuit.
+    We differentiate the expectation :math:`\langle Z\rangle` w.r.t. a single RY parameter and
     compare to a finite-difference estimate.
     """