### Install SKLearn and Requests

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/sklearn_svc.html

Installs the necessary libraries for the tutorial. Ensure you have scikit-learn and requests installed before proceeding.

```bash
pip install scikit-learn requests

```

--------------------------------

### Navigate to Examples Directory

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_windows.html

Change the current directory to 'examples' within the Docker container to access the provided scripts.

```bash
cd examples

```

--------------------------------

### Setup Backend and Imports

Source: https://tensorcircuit.readthedocs.io/en/latest/whitepaper/5-density-matrix.html

Imports necessary libraries and sets the backend for TensorCircuit. This is a common setup for most TensorCircuit simulations.

```python
import numpy as np
import tensorcircuit as tc

K = tc.set_backend("tensorflow")
```

--------------------------------

### Install Docker Desktop from Command Line

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_windows.html

Use this command to install Docker Desktop silently from the command line after downloading the installer.

```bash
"Docker Desktop Installer.exe" install
```

--------------------------------

### Install Dependencies

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/vqe_h2o.html

Install the necessary libraries for generating fermionic and qubit Hamiltonians. This includes openfermion and openfermionpyscf.

```bash
pip install openfermion openfermionpyscf
```

--------------------------------

### Setup Imports and Backend Configuration

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/torch_qml.html

Imports necessary libraries and sets the backend for TensorCircuit. This setup is required before defining quantum circuits or interfaces.

```python
import time
import numpy as np
import tensorflow as tf
import torch

import tensorcircuit as tc

K = tc.set_backend("tensorflow")

# Use TensorFlow as the backend, while wrapping the quantum function in the PyTorch interface
```

--------------------------------

### Install TensorCircuit (Linux x86)

Source: https://tensorcircuit.readthedocs.io/en/latest/quickstart.html

Use this command for a standard installation on Linux x86 systems. Ensure you have pip installed.

```bash
pip install tensorcircuit
```

--------------------------------

### Example: Setting Dense Layer Weights

Source: https://tensorcircuit.readthedocs.io/en/latest/api/applications/van.html

Demonstrates how to set the weights of a Dense layer using NumPy arrays obtained from another Dense layer. This involves getting weights from one layer and setting them to another.

```python
>>> layer_a = tf.keras.layers.Dense(1,
...   kernel_initializer=tf.constant_initializer(1.))
>>> a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))
>>> layer_a.get_weights()
[array([[1.],
       [1.],
       [1.]], dtype=float32), array([0.], dtype=float32)]
>>> layer_b = tf.keras.layers.Dense(1,
...   kernel_initializer=tf.constant_initializer(2.))
>>> b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))
>>> layer_b.get_weights()
[array([[2.],
       [2.],
       [2.]], dtype=float32), array([0.], dtype=float32)]
>>> layer_b.set_weights(layer_a.get_weights())
>>> layer_b.get_weights()
[array([[1.],
       [1.],

```

--------------------------------

### Install TensorCircuit Nightly Build

Source: https://tensorcircuit.readthedocs.io/en/latest/quickstart.html

To install the latest nightly build, first uninstall the stable version, then install the nightly package.

```bash
pip uninstall tensorcircuit

```

```bash
pip install tensorcircuit-nightly
```

--------------------------------

### tensorcircuit.about.about()

Source: https://tensorcircuit.readthedocs.io/en/latest/api/about.html

Prints the information for tensorcircuit installation and environment.

```APIDOC
## tensorcircuit.about.about()

### Description
Prints the information for tensorcircuit installation and environment.

### Method
Call

### Endpoint
N/A

### Parameters
None

### Request Example
```python
import tensorcircuit

tensorcircuit.about.about()
```

### Response
None (prints to console)
```

--------------------------------

### Setup and Imports for Classical Shadows

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/classical_shadows.html

Imports necessary libraries and sets the backend and data type for TensorCircuit operations. This setup is required before implementing classical shadows.

```python
import tensorcircuit as tc
from tensorcircuit import shadows
import numpy as np
from functools import partial
import time
import matplotlib.pyplot as plt

tc.set_backend("jax")
tc.set_dtype("complex128")
```

--------------------------------

### Minimal VMAP Example

Source: https://tensorcircuit.readthedocs.io/en/latest/whitepaper/6-3-vmap.html

This snippet shows a minimal example of VMAP usage. It demonstrates the output format for complex numbers.

```python
1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,
          -2.3792996e-08-7.8779987e-09j]]], dtype=complex64)>)
```

--------------------------------

### Install Tensorcircuit

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_Mac.html

Installs the Tensorcircuit Python package using pip.

```bash
pip install tensorcircuit

```

--------------------------------

### Install Docker Desktop with Windows Command Prompt

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_windows.html

This command is used to install Docker Desktop when using the Windows Command Prompt.

```cmd
start /w "" "Docker Desktop Installer.exe" install
```

--------------------------------

### Install TensorCircuit in Develop Mode

Source: https://tensorcircuit.readthedocs.io/en/latest/contribution.html

Install your local fork of TensorCircuit in develop mode to immediately test code modifications.

```bash
python setup.py develop
```

--------------------------------

### Install Development Dependencies

Source: https://tensorcircuit.readthedocs.io/en/latest/contribution.html

Install the necessary Python packages for local development, including core requirements and development-specific tools.

```bash
pip install -r requirements/requirements.txt
pip install -r requirements/requirements-dev.txt
```

--------------------------------

### Run Noisy QML Example

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_windows.html

Execute the 'noisy_qml.py' script using Python to observe its output. This is an example of running a TensorCircuit script within the Docker environment.

```python
python noisy_qml.py

```

--------------------------------

### Install Python Package

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_Mac.html

Use this command to install various Python packages, including TensorCircuit backends like Jax and PyTorch.

```bash
pip install [Package Name]

```

--------------------------------

### Example of eigsh_lanczos with JIT compilation

Source: https://tensorcircuit.readthedocs.io/en/latest/api/backends/jax_backend.html

Demonstrates how to use eigsh_lanczos with JAX. The first example shows efficient JIT compilation when the linear operator A remains constant across iterations. The second example illustrates inefficient JIT compilation when A changes in each iteration, leading to performance degradation.

```python
import jax
import numpy as np
def A(H,x):
    return jax.np.dot(H,x)

for n in range(100):
    
H = jax.np.array(np.random.rand(10,10))
x = jax.np.array(np.random.rand(10,10))
res = eigsh_lanczos(A, [H],x) #jitting is triggerd only at n=0

```

```python
import jax
import numpy as np
for n in range(100):
    
    def A(H,x):
    
        return jax.np.dot(H,x)
    H = jax.np.array(np.random.rand(10,10))
    x = jax.np.array(np.random.rand(10,10))
    res = eigsh_lanczos(A, [H],x) #jitting is triggerd at every step n

```

--------------------------------

### Example of JIT compilation with eigsh (jit once)

Source: https://tensorcircuit.readthedocs.io/en/latest/api/backends/jax_backend.html

This example illustrates the use of the `eigsh` function with JAX's JIT compilation. JIT compilation is invoked only once at the start, as the Python ID of the matrix-vector product function `A` is consistent throughout the loop.

```python
import jax
import numpy as np
def A(H,x):
    return jax.np.dot(H,x)

for n in range(100):
    
H = jax.np.array(np.random.rand(10,10))
    x = jax.np.array(np.random.rand(10,10))
    res = eigsh(A, [H],x) #jitting is triggerd only at n=0

```

--------------------------------

### Setup for Quantum Dropout Tutorial

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa_quantum_dropout.html

Imports necessary libraries and sets up backend and parameters for the QAOA and quantum dropout simulation. Includes setting the number of layers, circuits, and dropout ratio.

```python
import tensorcircuit as tc
import optax
import jax.numpy as jnp
import tensorflow as tf
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np
from functools import partial
from IPython.display import clear_output
import random

K = tc.set_backend("jax")

nlayers = 30  # the number of layers
ncircuits = 6  # six circuits with different initial parameters are going to be optimized at the same time
R = 0.5  # dropout ratio, 0 means no dropout, 1 means all dropout

```

--------------------------------

### Get Logical-Physical Mapping from Qiskit

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/compiler/qiskit_compiler.html

Determines the logical-to-physical qubit mapping by comparing a Qiskit QuantumCircuit before and after compilation. If the 'before' circuit is not provided, it assumes a default 'measure(q, q)' setup.

```python
def _get_logical_physical_mapping_from_qiskit(
    qc_after: Any,
    qc_before: Any = None
) -> Dict[int, int]:
    """
    get ``logical_physical_mapping`` from qiskit Circuit by comparing the circuit after and before compiling

    :param qc_after: qiskit ``QuantumCircuit`` after compiling
    :type qc_after: Any
    :param qc_before: qiskit ``QuantumCircuit`` before compiling,
        if None, measure(q, q) is assumed
    :type qc_before: Any
    :return: logical_physical_mapping
    :rtype: Dict[int, int]
    """
    logical_physical_mapping = {}
    for inst in qc_after.data:
        if inst[0].name == "measure":
            if qc_before is None:
                logical_q = qc_after.find_bit(inst[2][0]).index
            else:
                for instb in qc_before.data:
                    if (
                        instb[0].name == "measure"
                        and qc_before.find_bit(instb[2][0]).index
                        == qc_after.find_bit(inst[2][0]).index
                    ):
                        logical_q = qc_before.find_bit(instb[1][0]).index
                        break
            logical_physical_mapping[logical_q] = qc_after.find_bit(inst[1][0]).index
    return logical_physical_mapping
```

--------------------------------

### JIT Compilation and Gradient Calculation

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/circuit_basics.html

JIT compiles a function for acceleration. The first run may be slow, but subsequent evaluations are fast. This example shows how to get both the value and gradient of an energy function.

```python
energy_vag_jit = K.jit(K.value_and_grad(energy))

print(energy_vag_jit(params))
```

--------------------------------

### Get Layer Weights Example

Source: https://tensorcircuit.readthedocs.io/en/latest/api/keras.html

Demonstrates how to retrieve the weights of a Keras layer and set the weights of another layer using the retrieved values. This is useful for transferring learned parameters between models or layers.

```python
>>> layer_a = tf.keras.layers.Dense(1,
...   kernel_initializer=tf.constant_initializer(1.))
>>> a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))
>>> layer_a.get_weights()
[array([[1.],
       [1.],
       [1.]], dtype=float32), array([0.], dtype=float32)]
>>> layer_b = tf.keras.layers.Dense(1,
...   kernel_initializer=tf.constant_initializer(2.))
>>> b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))
>>> layer_b.get_weights()
[array([[2.],
       [2.],
       [2.]], dtype=float32), array([0.], dtype=float32)]
>>> layer_b.set_weights(layer_a.get_weights())
>>> layer_b.get_weights()
[array([[1.],
       [1.],
       [1.]], dtype=float32), array([0.], dtype=float32)]
```

--------------------------------

### Setup and Backend Configuration

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa_bo.html

Imports necessary libraries and configures the TensorCircuit backend with JAX, sets data types, and initializes the cotengra optimizer for efficient tensor network contraction. It also sets up the device for computation.

```python
import tensorcircuit as tc
from jax import numpy as jnp
import optax
import torch
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np
import cotengra as ctg
from typing import Union
import time
import odbo
from IPython.display import clear_output

K = tc.set_backend("jax")
tc.set_dtype("complex128")
dtype = torch.float64

# cotengra package to speed up the calculation
opt_ctg = ctg.ReusableHyperOptimizer(
    methods=["greedy", "kahypar"],
    parallel=True,
    minimize="combo",
    max_time=20,
    max_repeats=128,
    progbar=True,
)

tc.set_contractor("custom", optimizer=opt_ctg, preprocessing=True)

nlayers = 10
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
acqfn = "ucb"
```

--------------------------------

### Generate Heisenberg Hamiltonian

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/quantum.html

Generates a Heisenberg Hamiltonian with optional external fields (ZZ, XX, YY, Z, X, Y couplings). Requires TensorFlow to be installed. The example shows how to generate a Hamiltonian for a 1D line graph and extract its eigenvalues.

```python
def heisenberg_hamiltonian(
    g: Graph,
    hzz: float = 1.0,
    hxx: float = 1.0,
    hyy: float = 1.0,
    hz: float = 0.0,
    hx: float = 0.0,
    hy: float = 0.0,
    sparse: bool = True,
    numpy: bool = False,
) -> Tensor:
    """
    Generate Heisenberg Hamiltonian with possible external fields.
    Currently requires tensorflow installed

    :Example:

    >>> g = tc.templates.graphs.Line1D(6)
    >>> h = qu.heisenberg_hamiltonian(g, sparse=False)
    >>> tc.backend.eigh(h)[0][:10]
    array([-11.2111025,  -8.4721365,  -8.472136 ,  -8.472136 ,  -6.       ,
            -5.123106 ,  -5.123106 ,  -5.1231055,  -5.1231055,  -5.1231055],
        dtype=float32)

    :param g: input circuit graph
    :type g: Graph
    :param hzz: zz coupling, default is 1.0
    :type hzz: float
    :param hxx: xx coupling, default is 1.0
    :type hxx: float
    :param hyy: yy coupling, default is 1.0
    :type hyy: float
    :param hz: External field on z direction, default is 0.0
    :type hz: float

```

--------------------------------

### QAOA Solver Setup

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qubo_problem.html

Initializes parameters for the QAOA solver, including the number of layers and iterations. A callback function is defined to record the loss during training.

```python
iterations = 500
nlayers = 2

loss_list = []


def record_loss(loss, params):
    loss_list.append(loss)
```

--------------------------------

### Install Miniconda for Tensorflow

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_Mac.html

Installs Miniconda, which is recommended for installing Tensorflow optimized for MacOS (tensorflow-macos) or with GPU acceleration (tensorflow-metal). This script downloads and installs Miniconda, then activates the environment and installs Tensorflow dependencies.

```bash
curl -o ~/miniconda.sh https://repo.anaconda.com/miniconda/Miniconda3-latest-MacOSX-arm64.sh
bash ~/miniconda.sh -b -p $HOME/miniconda
source ~/miniconda/bin/activate
conda install -c apple tensorflow-deps

```

--------------------------------

### Setup Backend and Gates

Source: https://tensorcircuit.readthedocs.io/en/latest/whitepaper/6-2-pauli-string-expectation.html

Initializes the backend (TensorFlow or JAX) and imports necessary libraries. It also defines the `xx` gate matrix used in the ansatz circuit.

```python
import time
from functools import partial
import numpy as np
import tensorflow as tf
import tensornetwork as tn
import optax
import tensorcircuit as tc

K = tc.set_backend("tensorflow")

xx = tc.gates._xx_matrix  # xx gate matrix to be utilized
```

--------------------------------

### Setup and Imports for QAOA

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qubo_problem.html

Imports necessary libraries and sets up the backend for TensorCircuit. Ensures reproducibility by setting random seeds and specifying data types.

```python
import tensorcircuit as tc
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
import time

from tensorcircuit.applications.optimization import (
    QUBO_QAOA,
    QUBO_QAOA_cvar,
    cvar_loss,
)
from tensorcircuit.templates.ansatz import QAOA_ansatz_for_Ising
from tensorcircuit.templates.conversions import QUBO_to_Ising

K = tc.set_backend("tensorflow")
tf.random.set_seed(530)
tc.set_dtype("float32")
tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)
```

--------------------------------

### Instantiate and Call a Module

Source: https://tensorcircuit.readthedocs.io/en/latest/api/applications/van.html

Demonstrates how to instantiate a custom module and call it with input tensors. Shows how module names are prepended to variable names.

```python
>>> mod = MyModule()
>>> mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
>>> mod.w
<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>
```

--------------------------------

### Setup Imports and Backend Configuration

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/operator_spreading.html

Imports necessary libraries and sets the backend and data type for TensorCircuit operations. Ensure these are configured before running circuit simulations.

```python
import numpy as np
import tensorflow as tf
import tensorcircuit as tc
import matplotlib.pyplot as plt

tc.set_backend("tensorflow")
tc.set_dtype("complex128")
dtype = np.complex128
```

--------------------------------

### Install Vanilla Tensorflow

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_Mac.html

Installs the standard Tensorflow package developed by Google. Skip the Miniconda installation if you intend to use this version.

```bash
pip install tensorflow

```

--------------------------------

### Setup QAOA for NAE3SAT

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa_nae3sat.html

Imports necessary libraries and sets up backend and parameters for the QAOA optimization. This includes defining the number of layers and circuits to optimize concurrently.

```python
import tensorcircuit as tc
import optax
import tensorflow as tf
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np
from IPython.display import clear_output
import random

K = tc.set_backend("jax")

nlayers = 30  # the number of layers
ncircuits = 6  # six circuits with different initial parameters are going to be optimized at the same time

```

--------------------------------

### Setup TensorCircuit Backend

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/contractors.html

Initializes the TensorCircuit backend with TensorFlow and imports necessary libraries.

```python
import tensorcircuit as tc
import numpy as np
import cotengra as ctg
import opt_einsum as oem

K = tc.set_backend("tensorflow")
```

--------------------------------

### Create Range Tensor with CuPy

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/backends/cupy_backend.html

Creates a tensor with values ranging from start to stop with a given step, using CuPy's arange function. If stop is None, it defaults to start and starts from 0.

```python
def arange(self, start: int, stop: Optional[int] = None, step: int = 1) -> Tensor:
        if stop is None:
            return cp.arange(start=0, stop=start, step=step)
        return cp.arange(start=start, stop=stop, step=step)
```

--------------------------------

### Setup TensorCircuit Environment

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/portfolio_optimization.html

Imports necessary libraries and sets the backend for TensorCircuit. Configure TensorFlow logging to reduce verbosity.

```python
import tensorcircuit as tc
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt

from tensorcircuit.templates.ansatz import QAOA_ansatz_for_Ising
from tensorcircuit.templates.conversions import QUBO_to_Ising
from tensorcircuit.applications.optimization import QUBO_QAOA, QAOA_loss
from tensorcircuit.applications.finance.portfolio import StockData, QUBO_from_portfolio

K = tc.set_backend("tensorflow")
tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)
```

--------------------------------

### Install Docker Desktop with PowerShell

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_windows.html

This command is used to install Docker Desktop when using PowerShell.

```powershell
Start-Process '.inuild
ew-docker-desktop-installer.exe' -Wait install
```

--------------------------------

### Get QuVector Representation

Source: https://tensorcircuit.readthedocs.io/en/latest/api/densitymatrix.html

Gets the representation of the output state as a `QuVector` without computing the circuit.

```APIDOC
## quvector

### Description
Get the representation of the output state in the form of `QuVector` while maintaining the circuit uncomputed

### Returns

#### Success Response
- **QuVector** - `QuVector` representation of the output state from the circuit
```

--------------------------------

### Setup and Backend Configuration

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/barren_plateaus.html

Initializes the TensorFlow backend and sets the complex data type for TensorCircuit operations. Imports necessary libraries.

```python
import numpy as np
import tensorflow as tf
import tensorcircuit as tc

tc.set_backend("tensorflow")
tc.set_dtype("complex64")

Rx = tc.gates.rx
Ry = tc.gates.ry
Rz = tc.gates.rz

```

--------------------------------

### Setup Backend and Imports

Source: https://tensorcircuit.readthedocs.io/en/latest/whitepaper/4-gradient-optimization.html

Import necessary libraries and set the backend for TensorCircuit. This is a prerequisite for using TensorCircuit functionalities.

```python
import numpy as np
import scipy.optimize as optimize
import tensorflow as tf
import tensorcircuit as tc

K = tc.set_backend("tensorflow")
```

--------------------------------

### Initialize TensorCircuit and Parameters

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa.html

Sets up the TensorCircuit backend and defines global parameters for the QAOA simulation, including the number of layers, circuits to optimize, and nodes in the graph.

```python
import tensorcircuit as tc
import tensorflow as tf
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np
from IPython.display import clear_output
import random

K = tc.set_backend("tensorflow")

nlayers = 3  # the number of layers
ncircuits = 6  # six circuits with different initial parameters are going to be optimized at the same time
nnodes = 8  # the number of nodes

```

--------------------------------

### Setup TensorCircuit Backend

Source: https://tensorcircuit.readthedocs.io/en/latest/whitepaper/6-3-vmap.html

Sets the backend for TensorCircuit and prints the version. Imports numpy and tensorcircuit.

```python
import numpy as np
import tensorcircuit as tc

tc.set_backend("tensorflow")
print(tc.__version__)

nwires = 5
nlayers = 2
batch = 6
```

--------------------------------

### TensorCircuit Setup

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/mera.html

Initializes TensorCircuit with the TensorFlow backend and complex128 data type. This setup is required before defining quantum circuits.

```python
import numpy as np
import tensorflow as tf
import tensorcircuit as tc

tc.set_backend("tensorflow")
tc.set_dtype("complex128")
```

--------------------------------

### Initialize QuantumNet with a Quantum Function

Source: https://tensorcircuit.readthedocs.io/en/latest/api/torchnn.html

This example demonstrates how to wrap a quantum function (qpred) with QuantumNet. The quantum function defines a quantum circuit and calculates expectation values. QuantumNet takes the quantum function and its weights shape as input.

```python
K = tc.set_backend("tensorflow")

n = 6
nlayers = 2
batch = 2

def qpred(x, weights):
    c = tc.Circuit(n)
    for i in range(n):
        c.rx(i, theta=x[i])
    for j in range(nlayers):
        for i in range(n - 1):
            c.cnot(i, i + 1)
        for i in range(n):
            c.rx(i, theta=weights[2 * j, i])
            c.ry(i, theta=weights[2 * j + 1, i])
    ypred = K.stack([c.expectation_ps(x=[i]) for i in range(n)])
    ypred = K.real(ypred)
    return ypred

ql = tc.torchnn.QuantumNet(qpred, weights_shape=[2*nlayers, n])

ql(torch.ones([batch, n]))

```

--------------------------------

### Initialize Jax Backend

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensornetwork/backends/jax/jax_backend.html

Initializes the Jax backend, setting up necessary imports and configurations. Ensure Jax is installed before using this backend.

```python
import numpy as np
from typing import Optional, Text, Union, Sequence, Tuple

from tensornetwork.backends import abstract_backend
from tensornetwork.backends.jax import decompositions

Tensor = np.ndarray

_CACHED_MATVECS = {}
_CACHED_FUNCTIONS = {}

class JaxBackend(abstract_backend.AbstractBackend):
  """See abstract_backend.AbstractBackend for documentation."""

  def __init__(self, dtype: Optional[np.dtype] = None,
               precision: Optional[Text] = None) -> None:
    # pylint: disable=global-variable-undefined
    global libjax  # Jax module
    global jnp  # jax.numpy module
    global jsp  # jax.scipy module
    super().__init__()
    try:
      #pylint: disable=import-outside-toplevel
      import jax
    except ImportError as err:
      raise ImportError("Jax not installed, please switch to a different "
                        "backend or install Jax.") from err
    libjax = jax
    jnp = libjax.numpy
    jsp = libjax.scipy
    self.name = "jax"
    self._dtype = np.dtype(dtype) if dtype is not None else None
    self.jax_precision = precision if precision is not None else libjax.lax.Precision.DEFAULT #pylint: disable=line-too-long
```

--------------------------------

### JaxBackend Initialization

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/backends/jax_backend.html

Initializes the JaxBackend, setting up necessary JAX modules and checking for optional dependencies like optax.

```APIDOC
## JaxBackend()

### Description
Initializes the JaxBackend. This involves importing JAX and its submodules (numpy, scipy), and optionally optax. It also sets up global variables for these modules.

### Method
__init__

### Parameters
None

### Request Example
```python
b = JaxBackend()
```

### Response
None
```

--------------------------------

### Initialize QAOA Optimizer and Loss Tracking

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa.html

Sets up initial parameters, an optimizer (Adam), and a list to track losses for multiple circuits during QAOA optimization.

```python
params = K.implicit_randn(
    shape=[ncircuits, 2 * nlayers], stddev=0.1
)  # initial parameters
opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))

list_of_loss = [[] for i in range(ncircuits)]
```

--------------------------------

### Robust JSON GET Request

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/cloud/utils.html

Performs a GET request and returns the JSON response, with built-in retry logic for network issues.

```python
@reconnect()
def rget_json(*args: Any, **kws: Any) -> Any:
    r = requests.get(*args, **kws)
    return r.json()
```

--------------------------------

### Set Up Custom Contractors

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/cons.html

Demonstrates how to configure TensorCircuit contractors with custom optimizers and parameters. This includes setting up cotengra for hyperoptimization and opt_einsum for greedy contraction strategies.

```python
import cotengra as ctg
import opt_einsum as oem
import tensorcircuit as tc
import sys

sys.setrecursionlimit(10000) # for successfullt ctg parallel

opt = ctg.ReusableHyperOptimizer(
    methods=["greedy", "kahypar"],
    parallel=True,
    minimize="write",
    max_time=30,
    max_repeats=4096,
    progbar=True,
)
tz.set_contractor("custom", optimizer=opt, preprocessing=True)
tz.set_contractor("custom_stateful", optimizer=oem.RandomGreedy, max_time=60, max_repeats=128, minimize="size")
tz.set_contractor("plain-experimental", local_steps=3)
```

--------------------------------

### Robust GET Request

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/cloud/utils.html

A robust GET request function that automatically retries on connection errors and sets appropriate headers and timeouts.

```python
rget = reconnect()(requests.get)
```

--------------------------------

### from_qsim_file

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/abstractcircuit.html

Class method to initialize an AbstractCircuit from a Qsim file. Parses the file content to reconstruct the circuit.

```APIDOC
## from_qsim_file

### Description
Initialize an AbstractCircuit from a Qsim file.

### Parameters
- file (str): The path to the Qsim file.
- circuit_params (Optional[Dict[str, Any]]): Optional dictionary of parameters to initialize the circuit.

### Returns
- AbstractCircuit: An instance of AbstractCircuit initialized from the Qsim file.
```

--------------------------------

### Get Current Default Device

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/cloud/apis.html

Gets the current default quantum device without changing it globally. This is an alias for `set_device(set_global=False)`.

```python
get_device()
```

--------------------------------

### Switch Backend to JAX

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/tfim_vqe.html

Demonstrates how to switch the TensorCircuit backend to JAX at runtime. This allows for using JAX's features without modifying the core code.

```python
tc.set_backend("jax")  # change to jax backend
```

--------------------------------

### Get Current Default Provider

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/cloud/apis.html

Gets the current default cloud provider without changing it globally. This is an alias for `set_provider(set_global=False)`.

```python
get_provider()
```

--------------------------------

### Pauli String Expectation Example

Source: https://tensorcircuit.readthedocs.io/en/latest/api/mpscircuit.html

Example demonstrating the calculation of Pauli string expectation for a 2-qubit circuit with X and H gates.

```python
>>> c = tc.Circuit(2)
>>> c.X(0)
>>> c.H(1)
>>> c.expectation_ps(x=[1], z=[0])
array(-0.99999994+0.j, dtype=complex64)
```

--------------------------------

### Initialize QAOA Training Parameters

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/portfolio_optimization.html

Sets up the parameters for the Quantum Approximate Optimization Algorithm (QAOA), including the number of training iterations and layers for the ansatz. It also defines a callback function to record the loss during training.

```python
iterations = 1000
nlayers = 12
loss_list = []


# define a callback function to recode the loss
def record_loss(loss, params):
    loss_list.append(loss)
```

--------------------------------

### CuPyBackend Initialization

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/backends/cupy_backend.html

Initializes the CuPy backend. It checks for CuPy installation and raises an error if not found.

```APIDOC
## CuPyBackend()

### Description
Initializes the CuPy backend. Requires CuPy to be installed.

### Method
`__init__`

### Parameters
None

### Request Example
```python
b = CuPyBackend()
```

### Response
Initializes the backend with CuPy and CuPyX modules.
```

--------------------------------

### Initialize Jax Backend

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/backends/jax_backend.html

Initializes the Jax backend, importing necessary libraries like jax, jax.scipy, and optionally optax. Raises an ImportError if Jax is not installed.

```python
def __init__(self) -> None:
        global libjax  # Jax module
        global jnp  # jax.numpy module
        global jsp  # jax.scipy module
        global sparse  # jax.experimental.sparse
        global optax  # optax
        super(JaxBackend, self).__init__()
        try:
            import jax
        except ImportError:
            raise ImportError(
                "Jax not installed, please switch to a different "
                "backend or install Jax."
            )
        import jax.scipy
        from jax.experimental import sparse

        try:
            import optax

        except ImportError:
            logger.warning(
                "optax not installed, `optimizer` from jax backend cannot work"
            )
        libjax = jax
        jnp = libjax.numpy
        jsp = libjax.scipy

        self.name = "jax"
```

--------------------------------

### Initialize PyTorch Backend

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensornetwork/backends/pytorch/pytorch_backend.html

Initializes the PyTorch backend. Requires PyTorch to be installed. If not found, it raises an ImportError.

```python
class PyTorchBackend(abstract_backend.AbstractBackend):
  """See base_backend.BaseBackend for documentation."""

  def __init__(self) -> None:
    super().__init__()
    # pylint: disable=global-variable-undefined
    global torchlib
    try:
      # pylint: disable=import-outside-toplevel
      import torch
    except ImportError as err:
      raise ImportError("PyTorch not installed, please switch to a different "
                        "backend or install PyTorch.") from err
    torchlib = torch
    self.name = "pytorch"
```

--------------------------------

### Expectation Value Calculation Example

Source: https://tensorcircuit.readthedocs.io/en/latest/api/circuit.html

Demonstrates calculating expectation values with Pauli X and Y operators, including an example with readout error correction.

```python
>>> c = tc.Circuit(2)
>>> c.H(0)
>>> c.rx(1, theta=np.pi/2)
>>> c.sample_expectation_ps(x=[0], y=[1])
-0.99999976
>>> readout_error = []
>>> readout_error.append([0.9,0.75])
>>> readout_error.append([0.4,0.7])
>>> c.sample_expectation_ps(x=[0], y=[1],readout_error = readout_error)
```

--------------------------------

### Example Circuit Block

Source: https://tensorcircuit.readthedocs.io/en/latest/quickstart.html

Demonstrates the usage of a pre-defined example block within a TensorCircuit circuit. This serves as a shortcut for common circuit structures.

```python
c = tc.Circuit(4)
c = tc.templates.blocks.example_block(c, tc.backend.ones([16]))

```

--------------------------------

### Initialize and Run Optimization in Python

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/optimization_and_expressibility.html

Initializes the parameters for the variational quantum circuit and calls the main optimization function. This snippet demonstrates how to set up the initial state and execute the training process.

```python
v = tf.random.uniform([num_trial, L, N], minval=0.0, maxval=2 * np.pi, dtype=tf.float64)
E_initial, E_final, S_initial, S_final = opt_main(v)
```

--------------------------------

### Initialize DARBO Optimizer

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa_bo.html

Instantiates the DARBO_optimizer with specified parameters and prints the initial mode. This setup is for a 'small' mode optimization.

```python
mode = "small"

darbo_opt = DARBO_optimizer(
    eval_objective, 2 * nlayers, tr_length, failure_tolerance, mode, device
)
print(f"initial mode: {darbo_opt.get_mode()}")
```

--------------------------------

### Import Libraries and Print Version

Source: https://tensorcircuit.readthedocs.io/en/latest/whitepaper/6-4-quoperator.html

Imports necessary libraries (numpy, tensornetwork, tensorcircuit) and prints the installed tensorcircuit version. Ensure tensorcircuit is installed before running.

```python
import numpy as np
import tensornetwork as tn
import tensorcircuit as tc

print(tc.__version__)
```

--------------------------------

### Circuit Class Initialization

Source: https://tensorcircuit.readthedocs.io/en/latest/api/circuit.html

Demonstrates how to initialize a Circuit object with a specified number of qubits.

```APIDOC
## Circuit Class

### Description
Represents a quantum circuit, allowing for the application of various quantum gates.

### Parameters
- **nqubits** (int) - The number of qubits in the circuit.
- **inputs** (Optional[Any]) - Optional inputs for the circuit.
- **mps_inputs** (Optional[tensorcircuit.quantum.QuOperator]) - Optional MPS inputs.
- **split** (Optional[Dict[str, Any]]) - Optional split dictionary.

### Example
```python
c = tc.Circuit(3)
```
```

--------------------------------

### Install Tensorflow Metal Plugin

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_Mac.html

Installs the tensorflow-metal PluggableDevice for enhanced Tensorflow performance on compatible MacOS hardware. This is an optional step and may not be recommended for all users.

```bash
pip install tensorflow-metal

```

--------------------------------

### from_qsim_file

Source: https://tensorcircuit.readthedocs.io/en/latest/api/basecircuit.html

Loads a circuit from a QSIM file.

```APIDOC
## from_qsim_file

### Description
Loads a circuit from a QSIM file.

### Method
classmethod

### Parameters
#### Path Parameters
- **file** (str) - Required - The path to the QSIM file.
- **circuit_params** (Optional[Dict[str, Any]]) - Optional - Additional parameters for circuit construction.
```

--------------------------------

### Switch Simulation Backends

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/circuit_basics.html

Demonstrates how to switch between different simulation backends like TensorFlow, JAX, and PyTorch. Note that full functionality may not be guaranteed on all backends.

```python
# we can easily switch simulation backends away from NumPy!

with tc.runtime_backend("tensorflow") as K:
    c = get_circuit(3)
    print(c.state())

with tc.runtime_backend("jax") as K:
    c = get_circuit(3)
    print(c.state())

with tc.runtime_backend("pytorch") as K:
    # best performance and full functionality are not guaranteed on pytorch backend
    c = get_circuit(3)
    print(c.state())
```

--------------------------------

### Verify Tensorflow Installation

Source: https://tensorcircuit.readthedocs.io/en/latest/contribs/development_Mac.html

This Python script verifies the Tensorflow installation by loading the CIFAR-100 dataset, defining a ResNet50 model, compiling it, and performing a short training run.

```python
import tensorflow as tf

cifar = tf.keras.datasets.cifar100
(x_train, y_train), (x_test, y_test) = cifar.load_data()
model = tf.keras.applications.ResNet50(
    include_top=True,
    weights=None,
    input_shape=(32, 32, 3),
    classes=100,)

loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
model.compile(optimizer="adam", loss=loss_fn, metrics=["accuracy"])
model.fit(x_train, y_train, epochs=5, batch_size=64)

```

--------------------------------

### example_block()

Source: https://tensorcircuit.readthedocs.io/en/latest/genindex.html

Provides an example block for circuit construction. Found in the tensorcircuit.templates.blocks module.

```APIDOC
## example_block()

### Description
Provides an example block for circuit construction.

### Module
tensorcircuit.templates.blocks
```

--------------------------------

### TensorFlow Arange Sequence

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/backends/tensorflow_backend.html

Creates a sequence of numbers with a specified start, stop, and step. If only one argument is provided, it's treated as the stop value starting from 0.

```python
def arange(self, start: int, stop: Optional[int] = None, step: int = 1) -> Tensor:
        if stop is None:
            return tf.range(start=0, limit=start, delta=step)
        return tf.range(start=start, limit=stop, delta=step)
```

--------------------------------

### Build Source Distribution and Wheel for PyPI

Source: https://tensorcircuit.readthedocs.io/en/latest/contribution.html

Create source distribution and wheel files for the project, which are necessary for uploading to PyPI.

```bash
python setup.py sdist bdist_wheel
export VERSION=0.x.y
twine upload dist/tensorcircuit-${VERSION}-py3-none-any.whl dist/tensorcircuit-${VERSION}.tar.gz

```

--------------------------------

### Conditional Measurement Example

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/basecircuit.html

Performs a conditional measurement on a specified qubit in the Z basis. This method is jittable and can return the measured result as an integer tensor. The example demonstrates its use with `conditional_gate` and `expectation`.

```python
c = tc.Circuit(2)
c.H(0)
r = c.cond_measurement(0)
c.conditional_gate(r, [tc.gates.i(), tc.gates.x()], 1)
c.expectation([tc.gates.z(), [0]]), c.expectation([tc.gates.z(), [1]])
# two possible outputs: (1, 1) or (-1, -1)
```

--------------------------------

### Initialize and Use MPSCircuit

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/mpscircuit.html

Demonstrates basic usage of MPSCircuit by initializing a 3-qubit circuit, applying single-qubit (Hadamard, RX) and two-qubit (CNOT) gates, and calculating an expectation value.

```python
mps = tc.MPSCircuit(3)
mps.H(1)
mps.CNOT(0, 1)
mps.rx(2, theta=tc.num_to_tensor(1.))
mps.expectation((tc.gates.z(), 2))
```

--------------------------------

### Load Circuit from Qsim File

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/abstractcircuit.html

The `from_qsim_file` class method allows loading a circuit definition from a file formatted according to the Qsim input specification. It automatically determines the number of qubits if not provided.

```python
@classmethod
    def from_qsim_file(
        cls,
        file: str,
        circuit_params: Optional[Dict[str, Any]] = None,
    ) -> "AbstractCircuit":
        with open(file, "r") as f:
            lines = f.readlines()
        if circuit_params is None:
            circuit_params = {}
        if "nqubits" not in circuit_params:
            circuit_params["nqubits"] = int(lines[0])

        c = cls(**circuit_params)
        c = cls._apply_qsim(c, lines)
        return c
```

--------------------------------

### tensorcircuit.cloud.abstraction.Task.status

Source: https://tensorcircuit.readthedocs.io/en/latest/genindex.html

Gets the status of the task.

```APIDOC
## status()

### Description
Gets the status of the task.

### Method
(tensorcircuit.cloud.abstraction.Task method)
```

--------------------------------

### tensorcircuit.mpscircuit.MPSCircuit.state

Source: https://tensorcircuit.readthedocs.io/en/latest/genindex.html

Gets the state of the MPSCircuit.

```APIDOC
## state()

### Description
Gets the state of the MPSCircuit.

### Method
(tensorcircuit.mpscircuit.MPSCircuit method)
```

--------------------------------

### VQE Optimization Loop

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/vqe_h2o.html

Sets up the optimizer and runs the VQE optimization loop for a specified number of steps. It prints the energy at intervals to monitor convergence.

```python
vags = tc.backend.jit(tc.backend.value_and_grad(vqe))
lr = tf.keras.optimizers.schedules.ExponentialDecay(
    decay_rate=0.5, decay_steps=300, initial_learning_rate=0.5e-2
)
opt = tc.backend.optimizer(tf.keras.optimizers.Adam(lr))

param = tc.backend.implicit_randn(shape=[depth, n, 4], stddev=0.02, dtype="float32")
for i in range(600):
    e, g = vags(param)
    param = opt.update(g, param)
    if i % 100 == 0:
        print(e)
```

--------------------------------

### tensorcircuit.densitymatrix.DMCircuit2.state

Source: https://tensorcircuit.readthedocs.io/en/latest/genindex.html

Gets the state of the DMCircuit2.

```APIDOC
## state()

### Description
Gets the state of the DMCircuit2.

### Method
(tensorcircuit.densitymatrix.DMCircuit2 method)
```

--------------------------------

### tensorcircuit.densitymatrix.DMCircuit.state

Source: https://tensorcircuit.readthedocs.io/en/latest/genindex.html

Gets the state of the DMCircuit.

```APIDOC
## state()

### Description
Gets the state of the DMCircuit.

### Method
(tensorcircuit.densitymatrix.DMCircuit method)
```

--------------------------------

### Device Initialization and Management

Source: https://tensorcircuit.readthedocs.io/en/latest/_modules/tensorcircuit/cloud/abstraction.html

Instantiate or retrieve a Device object. Devices can be specified with a name and an optional provider.

```python
d = Device.from_name("simulator", provider="local")
print(d)
```

--------------------------------

### Parallel Optimization with vmap and partial

Source: https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa_quantum_dropout.html

Optimizes QAOA circuits in parallel using JAX's vmap and partial for handling non-hashable graph weights. It includes initialization of parameters, optimizer setup, and the optimization loop.

```python
# use vvag to get the losses and gradients with different random circuit instances
QAOA_vvag = K.jit(
    K.vvag(partial(QAOAansatz_rnd, g=rnd_graphs_w), argnums=0, vectorized_argnums=0)
)

params_rnd = K.implicit_randn(
    shape=[ncircuits, 2 * nlayers], stddev=0.1
)  # initial parameters
if type(K).__name__ == "JaxBackend":
    opt = K.optimizer(optax.adam(1e-2))
else:
    opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))

list_of_loss = [[] for i in range(ncircuits)]

for i in range(2000):
    loss, grads = QAOA_vvag(params_rnd)
    params_rnd = opt.update(grads, params_rnd)  # gradient descent

    # visualise the progress
    clear_output(wait=True)
    list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))
    plt.xlabel("Iteration")
    plt.ylabel("Cost")
    for index in range(ncircuits):
        plt.plot(range(i + 1), list_of_loss[index])
    legend = [f"circuit {leg}" for leg in range(ncircuits)]
    plt.legend(legend)
    plt.show()
```