### Install Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Install the Qlasskit library using pip. This command is used to add the package to your Python environment.

```bash
pip install qlasskit
```

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

### Build and Serve Docs Locally

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

Install Sphinx and related packages, then navigate to the docs directory and build the HTML documentation locally to preview changes.

```bash
pip install sphinx sphinx_rtd_theme sphinx_rtd_dark_mode myst_nb
cd docs
make html
```

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

### Bind Custom Type Parameter to Qlassf Function

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/parameters.ipynb

Illustrates parameterization with custom and complex types like Qlist and Qint. The example binds a Qlist of Qints to a qlassf function and shows the resulting circuit expressions.

```python
from qlasskit import Qlist, Qint, Qint4


@qlassf
def test(a: Parameter[Qlist[Qint[2], 4]], b: Qint[4]) -> Qint[4]:
    s = Qint4(0)
    for n in a:
        s += n
    return s + b


qf = test.bind(a=[2, 1, 0, 3])
qf.expressions
```

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

### Run BQM on D-Wave Annealer

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/bqm.ipynb

Execute a BQM on a real D-Wave quantum annealer. Ensure you have a valid D-Wave account and configure the sampler accordingly. This example uses `EmbeddingComposite` for embedding the problem onto the QPU.

```python
from dwave.system import DWaveSampler, EmbeddingComposite

sampler = EmbeddingComposite(DWaveSampler())
sampleset = sampler.sample(bqm, num_reads=10)
decoded_samples = decode_samples(test_factor, sampleset)
best_sample = min(decoded_samples, key=lambda x: x.energy)
print(best_sample.sample)
```

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

### Build and Upload Release to PyPI

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

For maintainers, this process involves building the distribution packages and uploading them to PyPI using twine. Ensure build and twine are installed.

```bash
pip install build twine
rm -r dist/*
python -m build
python -m twine upload dist/*
```

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

### Clone Qlasskit Repository

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

Clone the Qlasskit repository locally to start contributing. Ensure you replace YOUR_USERNAME with your GitHub username.

```bash
git clone https://github.com/YOUR_USERNAME/qlasskit.git
```

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

### Export to Binary Quadratic Model with QlassF.to_bqm()

Source: https://context7.com/dakk/qlasskit/llms.txt

Converts a compiled function's boolean expression to various BQM formats (BQM, QUBO, Ising, PyQubo model) for use with quantum annealers or simulated annealing solvers. Requires `pip install pyqubo`. The example also shows solving with `dimod.SimulatedAnnealingSampler` and decoding the results.

```python
from qlasskit import qlassf, Qint
from qlasskit.bqm import decode_samples

@qlassf
def polynomial(x: Qint[4]) -> bool:
    return x * x == 9   # find x such that x^2 == 9

# Export to different BQM formats
bqm   = polynomial.to_bqm(fmt="bqm")    # dimod BQM
qubo  = polynomial.to_bqm(fmt="qubo")   # QUBO dict
ising = polynomial.to_bqm(fmt="ising")  # (h, J) Ising model
model = polynomial.to_bqm(fmt="pq_model")  # raw pyqubo model

# Solve with simulated annealing (requires dimod)
import dimod

sa     = dimod.SimulatedAnnealingSampler()
result = sa.sample(bqm, num_reads=100)
decoded = decode_samples(polynomial, result)

for sample in decoded[:3]:
    print(sample.energy, sample.sample)
    # e.g. 0.0  {'x': Qint4(3)}  — found x=3 since 3^2=9
```

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

### Simulate Quantum Circuit and Decode Results

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/quickstart.ipynb

Simulate the quantum circuit using AerSimulator, get the counts, and decode them into a human-readable format for plotting.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = sum_two_numbers.decode_counts(counts)
plot_histogram(counts_readable)
```

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

### Define and Print qlassf Function

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_unitary_of_f.ipynb

Defines a qlassf function and prints its representation. Ensure qlasskit is installed.

```python
from qlasskit import qlassf


@qlassf
def f(a: bool, b: bool) -> bool:
    return a ^ (not b)


print(f"\n{f}\n")
```

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

### Qlasskit with Qlist for Searching

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Shows how to use Qlist, a fixed-size list type, within Qlasskit functions. This example defines a 'search' function that checks if a given value exists in a list of 2-bit integers.

```python
@qlassf
def search(alist: Qlist[Qint[2], 4], to_search: Qint[2]):
  for x in alist:
    if x == to_search:
      return True
  return False
```

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

### Simulate and Get Unitary Matrix

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_unitary_of_f.ipynb

Uses AerSimulator with the 'unitary' method to obtain the unitary matrix of the quantum circuit. The result is then converted to LaTeX for display.

```python
from qiskit import transpile
from qiskit_aer import AerSimulator
from qiskit.visualization import array_to_latex

simulator = AerSimulator(method="unitary")
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
array_to_latex(result.get_unitary(circ, 3), max_size=16)
```

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

### Simulate and Analyze Deutsch-Jozsa Algorithm Results

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_deutsch_jozsa.ipynb

Measure all qubits, set up an Aer simulator, transpile the circuit, run the simulation, and get the measurement counts. Decode the counts using the algorithm's decoder and plot the histogram.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = q_algo.decode_counts(counts)
plot_histogram(counts_readable)
```

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

### Convert qlassf function to BQM

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/bqm.ipynb

Convert a qlassf function to a Binary Quadratic Model (BQM). This example binds a parameter and then converts the function to a BQM for further processing.

```python
from qlasskit import qlassf, Qint, Parameter


@qlassf
def test_factor_generic(num: Parameter[Qint[4]], a: Qint[3], b: Qint[3]) -> Qint[4]:
    return num - (a * b)


test_factor = test_factor_generic.bind(num=15)
bqm = test_factor.to_bqm()

print("Vars:", bqm.num_variables, "\nInteractions:", bqm.num_interactions)
```

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

### Grover's Search Algorithm Implementation

Source: https://context7.com/dakk/qlasskit/llms.txt

Builds a Grover's search circuit using a `QlassF` oracle. It automatically computes the optimal number of iterations and accepts either a boolean oracle or a generic function with an `element_to_search`. The example demonstrates exporting to Qiskit, running on `AerSimulator`, and decoding the results.

```python
from qlasskit import qlassf, Qint
from qlasskit.algorithms import Grover
from qiskit_aer import AerSimulator
from qiskit import transpile

# Oracle: returns True for the element we are searching for
@qlassf
def contains_7(x: Qint[4]) -> bool:
    return x == 7

algo = Grover(contains_7, True)

# Alternatively, search for a specific output value of a general function
@qlassf
def f(x: Qint[4]) -> Qint[4]:
    return x * 2

algo2 = Grover(f, element_to_search=14)  # find x such that f(x)==14

# Run on simulator
qc  = algo.export("qiskit")
sim = AerSimulator()
qc.measure_all()
result = sim.run(transpile(qc, sim), shots=1024).result()
counts = result.get_counts()

decoded = algo.decode_counts(counts, discard_lower=10)
print(decoded)   # {7: <high_count>}  — found x=7
```

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

### Create Feature Branch

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

Create a new branch for your changes, starting from the upstream main branch. Fetch upstream changes before creating the branch.

```bash
git fetch upstream
git checkout -b your-branch-name upstream/master
```

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

### Execute Grover Search with Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_hash.ipynb

Exports the Grover algorithm to a Qiskit quantum circuit, measures all qubits, simulates the circuit using AerSimulator, and plots the results. Requires Qiskit and Qiskit Aer to be installed.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

nc = q_algo.export("qiskit")
nc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = q_algo.decode_counts(counts, discard_lower=5)
plot_histogram(counts_readable)
```

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

### Define Realistic Sudoku Checker with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_sudoku.ipynb

Implements a Sudoku checker for a 4x4 matrix using Qlasskit's Qint for integer representation. This example highlights the significant increase in qubit requirements for more realistic Sudoku problems.

```python
from qlasskit import Qint, Qint3


@qlassf
def sudoku_check(m: Qmatrix[Qint[2], 4, 4]) -> bool:
    res = True

    # Constraints
    res = (m[0][2] == 3) and (m[0][0] == 1)

    # Check every row and column
    for i in range(len(m)):
        c = (Qint3(0) + m[i][0] + m[i][1] + m[i][2] + m[i][3]) == 6
        r = (Qint3(0) + m[0][i] + m[1][i] + m[2][i] + m[3][i]) == 6
        res = res and c and r

    return res


print(sudoku_check.circuit())
```

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

### Run Tox for Checks

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

Before committing, run tox to ensure type checking, linting, and tests pass. Ensure tox is installed via pip.

```bash
tox
```

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

### Qlasskit with Tuples and Fixed-Size Lists

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Illustrates the use of complex data types like tuples and fixed-size lists within Qlasskit functions. This example shows a function accepting a tuple of two 8-bit integers and returning a tuple of booleans.

```python
@qlassf
def f(a: Tuple[Qint[8], Qint[8]]) -> Tuple[bool, bool]:
  return a[0] == 42, a[1] == 0
```

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

### Create Oracle from Scratch

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_bernstein_vazirani.ipynb

Define a quantum oracle from scratch using Python and qlasskit's Qint for a 4-bit secret. This method allows for custom oracle logic.

```python
from qlasskit import qlassf, Qint


@qlassf
def oracle(x: Qint[4]) -> bool:
    s = Qint4(14)
    return (x[0] & s[0]) ^ (x[1] & s[1]) ^ (x[2] & s[2]) ^ (x[3] & s[3])


oracle.export("qiskit").draw("mpl")
```

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

### QCircuit Initialization

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.qcircuit.qcircuit.QCircuit.md

Initializes a quantum circuit with a specified number of qubits and an optional name.

```APIDOC
## QCircuit(num_qubits=0, name='qc', native=None)

### Description
Initialize a quantum circuit.

### Parameters
#### Parameters
- **num_qubits** (*int*, optional) - The number of qubits in the circuit. Defaults to 0.
- **name** (*str*, optional) - The name of the circuit. Defaults to 'qc'.
- **native** (*any*, optional) - Represents native gate set. Defaults to None.
```

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

### Initialize Grover Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/algorithms.ipynb

Instantiate the `Grover` algorithm by providing a quantum oracle function decorated with `@qlassf` and a boolean flag. The oracle defines the search space.

```python
from qlasskit.algorithms import Grover


@qlassf
def g_orac(a: Tuple[bool, bool]) -> bool:
    return a[0] and not a[1]


q_algo = Grover(g_orac, True)
```

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

### Initialize Simon Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/algorithms.ipynb

Create an instance of the `Simon` algorithm by passing a function `f` decorated with `@qlassf`. This function defines the mapping for the periodicity search.

```python
from qlasskit.algorithms import Simon


@qlassf
def f(a: Qint[4]) -> Qint[4]:
    return (a >> 3) + 1


q_algo = Simon(f)
```

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

### Initialize Simon Algorithm with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_simon.ipynb

Initializes the Simon algorithm from Qlasskit, passing the previously defined quantum function 'f' to it.

```python
from qlasskit.algorithms import Simon

q_algo = Simon(f)
```

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

### Using py2qasm to Convert Python to QASM

Source: https://context7.com/dakk/qlasskit/llms.txt

Illustrates the usage of the `py2qasm` command-line tool for converting Python functions decorated with `@qlassf` into QASM (Quantum Assembly) format. Allows specifying the number of qubits and the compiler backend.

```bash
# py2qasm: translate a Python function to QASM
echo "
from qlasskit import qlassf
@qlassf
def g(a: bool, b: bool) -> bool:
    return a and b
" | py2qasm -e g -q 3.0
```

```bash
# py2qasm with file I/O and specific compiler
py2qasm -i circuit.py -e my_circuit -o out.qasm -c internal -q 2.0
```

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

### Simulate and Decode Results with QlassKit

Source: https://context7.com/dakk/qlasskit/llms.txt

Demonstrates how to simulate a quantum circuit using Qiskit Aer, retrieve raw counts, and decode them into a human-readable format using QlassKit's `decode_counts` method. Also shows exporting the QlassF to other frameworks.

```python
from qiskit_aer import AerSimulator
from qiskit import transpile

sim    = AerSimulator()
result = sim.run(transpile(qc, sim)).result()
counts = result.get_counts(qc)

readable = sum_two.decode_counts(counts)
# e.g. {Qint2(3): 1024}  — sum of 1+2 = 3

# Export to other frameworks
cirq_circ     = sum_two.export("cirq")
pennylane_dev = sum_two.export("pennylane")
qasm_str      = sum_two.export("qasm")
sympy_expr    = sum_two.export("sympy")
```

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

### Define a Quantum Function with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Define a classical function in Python decorated with `@qlassf` to be translated into quantum operators. This example shows a function 'h' that takes a 4-bit integer and returns a boolean.

```python
from qlasskit import qlassf, Qint 

@qlassf
def h(k: Qint[4]) -> bool:
    h = True
    for i in range(4):
        h = h and k[i]
    return h
```

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

### Using py2bexp to Convert Python to Boolean Expressions

Source: https://context7.com/dakk/qlasskit/llms.txt

Demonstrates how to use the `py2bexp` command-line tool to translate Python functions decorated with `@qlassf` into boolean expressions. Supports various output formats like CNF and DIMACS, and can read from stdin or files.

```bash
# py2bexp: translate a Python function to boolean expressions
echo "
from qlasskit import qlassf, Qint
@qlassf
def f(x: Qint[4]) -> bool:
    return x > 7
" | py2bexp -e f -f cnf -t sympy
```

```bash
# py2bexp with explicit input/output files
py2bexp -i my_function.py -e my_fn -o output.txt -f dnf -t dimacs
```

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

### QCircuit: Low-level Quantum Circuit Builder

Source: https://context7.com/dakk/qlasskit/llms.txt

Demonstrates the construction, manipulation, and export of quantum circuits using Qlasskit's internal QCircuit representation. Supports manual gate construction, named qubit maps, and composition.

```python
from qlasskit.qcircuit import QCircuit, gates

# Manual circuit construction
pc = QCircuit(3, name="my_circuit")
pc.h(0)
pc.cx(0, 1)
pc.ccx(0, 1, 2)
pc.barrier(label="mid")
pc.x(2)

print(qc)          # QCircuit<my_circuit>(4 gates, 3 qubits)
print(qc.gate_stats)   # {'H': 1, 'CX': 1, 'CCX': 1, 'X': 1}

# Named qubit access
pc2 = QCircuit(2)
pc2.add_qubit("ancilla")
pc2.h(qc2["ancilla"])

# Compose two circuits
combined = qc + qc2.copy(vanilla=True)

# Apply QFT
pc3 = QCircuit(4)
pc3.qft([0, 1, 2, 3])

# Export
qiskit_qc = qc.export(mode="circuit", framework="qiskit")
qasm_str  = qc.export(mode="circuit", framework="qasm")

# Random circuit for testing
rand_qc = QCircuit.random(qubits_n=5, depth=20)
```

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

### Parameterize and Bind Qlasskit Functions

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Demonstrates how to parameterize Qlasskit functions and bind values to these parameters before compilation. This allows for creating specialized versions of a function.

```python
@qlassf
def test(a: Parameter[bool], b: bool) -> bool:
    return a and b

qf = test.bind(a=True)
```

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

### Initialize Grover Algorithm for SAT

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_sat.ipynb

Initializes the Grover algorithm from qlasskit to search for inputs satisfying the defined SAT oracle. The target value is set to True. Requires importing Grover.

```python
from qlasskit.algorithms import Grover

q_algo = Grover(sat, True)
pc = q_algo.export("qiskit")
```

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

### Initialize Deutsch-Jozsa Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/algorithms.ipynb

Instantiate the `DeutschJozsa` algorithm by providing a function `f` decorated with `@qlassf`. This function represents the oracle to be tested for constant or balanced properties.

```python
from qlasskit.algorithms import DeutschJozsa


@qlassf
def f(b: Qint[4]) -> bool:
    return b < 16


q_algo = DeutschJozsa(f)
```

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

### Initialize Grover Search Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_hash.ipynb

Initializes the Grover search algorithm with the hash function and the target hash value. The target value must be an instance of `Qint8`.

```python
from qlasskit.algorithms import Grover

q_algo = Grover(hash_simp, Qint8(0xCA))
```

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

### Apply Bernstein-Vazirani Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_bernstein_vazirani.ipynb

Initialize and export the Bernstein-Vazirani quantum algorithm using a pre-defined oracle. This prepares the quantum circuit for execution.

```python
from qlasskit.algorithms import BernsteinVazirani

q_algo = BernsteinVazirani(oracle)
pc = q_algo.export("qiskit")
pc.draw("mpl")
```

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

### QlassF Class Constructor

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.qlassfun.QlassF.md

Initializes a new instance of the QlassF class.

```APIDOC
## 
### Description
Initializes a new instance of the QlassF class.

### Parameters
* **name** (str) - The name of the qlassf function.
* **original_f** (Callable) - The original function object.
* **args** (List[Arg]) - A list of arguments for the function.
* **returns** (Arg) - The return type of the function.
* **exps** (List[Tuple[Symbol, Boolean]]) - A list of expressions associated with the function.
```

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

### Execute Grover Search with Qiskit Aer Simulator

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover.ipynb

Prepare the Grover search circuit for execution by measuring all qubits, transpile it for the Aer simulator, run the simulation, and obtain the measurement counts. This snippet demonstrates how to use Qlasskit's Grover algorithm with a Qiskit backend.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)
```

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

### Grover Class Constructor

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.algorithms.grover.Grover.md

Initializes the Grover algorithm with a specified oracle and search parameters.

```APIDOC
## qlasskit.algorithms.grover.Grover(oracle: [QlassF](qlasskit.qlassfun.QlassF.md#qlasskit.qlassfun.QlassF), element_to_search: Qtype | None = None, n_iterations: int | None = None, n_matching: int = 1)

### Description
Initializes the Grover algorithm.

### Parameters
* **oracle** ([*QlassF*](qlasskit.qlassfun.QlassF.md#qlasskit.qlassfun.QlassF)) – The oracle function f(x) -> bool that returns True if x satisfies the condition, or a generic function f(x) = y to compare with element_to_search.
* **element_to_search** (*Qtype* *,* *optional*) – The element to search for within the search space.
* **n_iterations** (*int* *,* *optional*) – Forces a specific number of iterations. If not provided, it defaults to approximately pi/4 * sqrt(N/n_matching).
* **n_matching** (*int*) – The expected number of matching elements. Defaults to 1.
```

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

### Qlasskit Quantum Types: Qint and Qfixed

Source: https://context7.com/dakk/qlasskit/llms.txt

Illustrates the use of Qlasskit's quantum integer (Qint) and fixed-point (Qfixed) types in function signatures for circuit synthesis. These types define statically sized quantum bit vectors.

```python
from qlasskit import qlassf, Qint, Qfixed, Qchar
from qlasskit.types import Qlist, Qmatrix
from typing import Tuple

# Qint[N] — N-bit unsigned integer (N: 2,3,4,5,6,7,8,12,16)
@qlassf
def arith(a: Qint[4], b: Qint[4]) -> Qint[4]:
    return (a + b) * 2 - 1

# Qfixed[i,f] — fixed-point rational with i integer bits and f fractional bits
@qlassf
def scale(x: Qfixed[2, 4]) -> bool:
    return x > 1.5
```

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

### Initialize Deutsch-Jozsa Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_deutsch_jozsa.ipynb

Initialize the Deutsch-Jozsa algorithm with the defined quantum function `f`.

```python
from qlasskit.algorithms import DeutschJozsa

q_algo = DeutschJozsa(f)
```

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

### Export QlassF Circuit to Quantum Frameworks

Source: https://context7.com/dakk/qlasskit/llms.txt

Use the `.export()` method to export the compiled circuit to formats like Qiskit, Cirq, PennyLane, QASM, Sympy, or QuTiP. You can export the full circuit or a reusable gate.

```python
from qlasskit import qlassf, Qint

@qlassf
def sum_two(a: Qint[2], b: Qint[2]) -> Qint[2]:
    return a + b

# Export as a Qiskit QuantumCircuit
qiskit_circ = sum_two.export("qiskit")
qiskit_circ.draw("mpl")

# Export as a Qiskit Gate (for embedding into larger circuits)
from qiskit import QuantumCircuit
from qlasskit import Qint2

pc = QuantumCircuit(sum_two.num_qubits, len(sum_two.output_qubits))
pc.initialize(sum_two.encode_input(Qint2(1), Qint2(2)), sum_two.input_qubits)
pc.append(sum_two.gate("qiskit"), sum_two.qubits)
pc.measure(sum_two.output_qubits, range(len(sum_two.output_qubits)))

```

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

### Qlasskit Type Definitions and Functions

Source: https://context7.com/dakk/qlasskit/llms.txt

Demonstrates the use of Qlasskit's type system for defining functions that operate on specific data types like Qchar, Qlist, Tuple, and Qmatrix. These functions are decorated with @qlassf to be compilable.

```python
from qlasskit import qlassf, Qchar, Qlist, Qint, Qmatrix
from typing import Tuple

# Qchar — single ASCII character (8 bits)
@qlassf
def is_uppercase(c: Qchar) -> bool:
    return ord(c) >= 65 and ord(c) <= 90

# Qlist[T, N] — fixed-size list of N elements of type T
@qlassf
def list_sum(nums: Qlist[Qint[4], 3]) -> Qint[4]:
    return nums[0] + nums[1] + nums[2]

# Tuple — heterogeneous container
@qlassf
def swap_pair(p: Tuple[bool, Qint[4]]) -> Tuple[Qint[4], bool]:
    return p[1], p[0]

# Qmatrix[T, m, n] — m×n matrix
@qlassf
def trace_bool(m: Qmatrix[bool, 2, 2]) -> bool:
    return m[0][0] and m[1][1]
```

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

### Simon Class Initialization

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.algorithms.simon.Simon.md

Initializes the Simon algorithm with a given function f.

```APIDOC
## qlasskit.algorithms.simon.Simon(f: QlassF)

### Description
Initializes the Simon algorithm with the function f(x).

### Parameters
#### Parameters
- **f** (QlassF) - Required - The function f(x) to be used in the algorithm.
```

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

### Export and Simulate Quantum Circuit with Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_subset.ipynb

Exports the configured Grover algorithm to a Qiskit quantum circuit, adds measurements, and simulates it using AerSimulator. The results are then decoded for human readability and plotted as a histogram.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc = q_algo.export("qiskit")
pc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = q_algo.decode_counts(counts)
plot_histogram(counts_readable)
```

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

### ECDSA Key Generation, Signing, and Verification

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_ecdsa.ipynb

This snippet shows how to generate a private and public key pair, sign a message using the private key, and verify the signature using the public key. Note that the modular inverse function is highly simplified and only works for the specific parameters used.

```python
import random

# Extremely simplified parameters
P = 3  # Prime field
G = 2  # Generator
N = 3  # Order of generator


def mod_inv(a, m):
    return 1 if a == 1 else 2  # Only valid for P = 3


def generate_keypair():
    private_key = random.randint(1, 3)  # 2-bit key (1 to 3)
    public_key = pow(G, private_key, P)
    return private_key, public_key


def sign(message, private_key):
    z = message % N
    k = random.randint(1, 3)  # 2-bit nonce
    r = pow(G, k, P)
    s = (mod_inv(k, N) * (z + r * private_key)) % N
    return (r, s)


def verify(message, signature, public_key):
    r, s = signature
    z = message % N
    w = mod_inv(s, N)
    u1 = (z * w) % N
    u2 = (r * w) % N
    v = (pow(G, u1, P) * pow(public_key, u2, P)) % P
    return v == r


# Example usage
private_key, public_key = generate_keypair()
message = int("0b0", 2)  # Single character message
signature = sign(message, private_key)
is_valid = verify(message, signature, public_key)

print(f"Private Key: {private_key}")
print(f"Public Key: {public_key}")
print(f"Message: {message}")
print(f"Signature: {signature}")
print(f"Signature valid: {is_valid}")
```

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

### Define a Big Circuit with fastOptimizer

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_big_circuit.ipynb

Use `qlassfa` with `boolopt.fastOptimizer` to define a function that generates a large quantum circuit. This is recommended for performance when dealing with many qubits or complex operations.

```python
from qlasskit import Qint8, Qlist, boolopt, qlassfa


@qlassfa(bool_optimizer=boolopt.fastOptimizer)
def test(a_list: Qlist[Qint8, 64]) -> Qint8:
    h_val = Qint8(0)
    for c in a_list:
        h_val = h_val + c
    return h_val
```

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

### Initialize Grover Algorithm for Subset Sum

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_subset.ipynb

Initializes the Grover algorithm with the defined `subset_sum` function as the oracle. The `set_` parameter is bound to a specific list, and the target value is set. `n_matching` is specified to account for expected symmetric solutions (e.g., (i,j) and (j,i)).

```python
from qlasskit.algorithms import Grover

q_algo = Grover(subset_sum.bind(set_=[0, 5, 2, 3]), Qint3(7), n_matching=2)
```

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

### Print the Circuit Representation

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_big_circuit.ipynb

After defining the function, you can print its generated quantum circuit representation. This helps in understanding the scale and complexity of the circuit.

```python
print(test.circuit())
```

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

### Export and Simulate Grover's Algorithm with Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_factors.ipynb

Exports the Grover algorithm circuit to Qiskit, simulates it using AerSimulator, and decodes the results.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc = q_algo.export("qiskit")
pc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = q_algo.decode_counts(counts, discard_lower=5)
plot_histogram(counts_readable)
```

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

### Add Upstream Remote

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

Add the original Qlasskit repository as an upstream remote to keep your local copy synchronized with the main project.

```bash
git remote add upstream https://github.com/dakk/qlasskit.git
```

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

### Initialize Grover Search Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover.ipynb

Initialize the Grover search algorithm with the defined oracle function and the target output value. The `True` argument indicates that we are searching for an input that yields a `True` result from the oracle.

```python
from qlasskit.algorithms import Grover

q_algo = Grover(and_all, True)
```

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

### Export and Simulate Sudoku Solver with Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_sudoku.ipynb

Exports the Grover algorithm's quantum circuit to Qiskit, adds measurements, and simulates it using AerSimulator. The results are then decoded to a human-readable format, discarding low-probability outcomes.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc = q_algo.export("qiskit")
pc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = q_algo.decode_counts(counts, discard_lower=20)

plot_histogram(counts_readable)
```

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

### Simulate and Decode Bernstein-Vazirani Results

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_bernstein_vazirani.ipynb

Execute the Bernstein-Vazirani quantum circuit on a simulator, measure the qubits, and decode the results to find the secret string. This step involves running the circuit and interpreting the measurement counts.

```python
from qiskit import QuantumCircuit
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc.measure_all()
simulator = AerSimulator()
result = simulator.run(pc).result()
counts = result.get_counts(pc)

counts_readable = q_algo.decode_counts(counts)
plot_histogram(counts_readable)
```

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

### Create and Activate Pyenv Environment

Source: https://github.com/dakk/qlasskit/blob/master/CONTRIBUTING.md

Use pyenv to create and activate an isolated Python environment for working on Qlasskit. This helps manage dependencies effectively.

```bash
pyenv virtualenv qlasskit-env
```

```bash
pyenv activate qlasskit-env
```

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

### Solve BQM with Simulated Annealing

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_bqm_polynomial.ipynb

Use `neal.SimulatedAnnealingSampler` to find samples for the BQM. Decode the samples using `decode_samples` and find the sample with the minimum energy.

```python
import neal
from qlasskit.bqm import decode_samples

sa = neal.SimulatedAnnealingSampler()
sampleset = sa.sample(bqm, num_reads=10)
decoded_samples = decode_samples(poly, sampleset)
best_sample = min(decoded_samples, key=lambda x: x.energy)
print(best_sample.sample)
```

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

### Solve BQM using Simulated Annealing

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_bqm_tsp.ipynb

Solves the generated BQM using the Simulated Annealing sampler from the 'neal' library. The results are decoded to find the best sample representing the shortest path.

```python
import neal
from qlasskit.bqm import decode_samples

sa = neal.SimulatedAnnealingSampler()
sampleset = sa.sample(bqm, num_reads=10)
decoded_samples = decode_samples(tsp_f, sampleset)
best_sample = min(decoded_samples, key=lambda x: x.energy)
print(best_sample.sample, ":", best_sample.energy)
```

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

### Comparison Operators

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/supported.md

Demonstrates various comparison operators including greater than, less than or equal to, equal to, and not equal to.

```python
a > b or b <= c and c == d or c != a
```

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

### Define Toy Hash Function with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_hash.ipynb

Defines a simple hash function using qlasskit's decorator. Ensure all necessary qlasskit components are imported.

```python
from qlasskit import qlassf, Qint, Qint8, Qlist


@qlassf
def hash_simp(m: Qlist[Qint[4], 2]) -> Qint[8]:
    hv = 0
    for i in m:
        hv = ((hv << 4) ^ (hv >> 1) ^ i) & 0xFF

    return hv
```

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

### Compile Python Function to Quantum Circuit with @qlassf

Source: https://context7.com/dakk/qlasskit/llms.txt

Use the `@qlassf` decorator or `qlassf()` function to compile Python functions into `QlassF` objects. You can also pass the source code as a string. Options like `compiler` and `uncompute` can be specified.

```python
from qlasskit import qlassf, Qint, Qint4

# Basic usage as a decorator
@qlassf
def is_even(n: Qint[4]) -> bool:
    return n % 2 == 0

print(is_even)
# QlassF<is_even>(n:Qint4) -> bool:
#     _ret = ...

# As a regular function call (string source also accepted)
from qlasskit import qlassf, Qint2
f_str = "def add(a: Qint[2], b: Qint[2]) -> Qint[2]:\n    return a + b"
add = qlassf(f_str)

# Choosing a specific compiler backend
@qlassf(compiler="tweedledum")
def my_fn(x: bool) -> bool:
    return not x

# With uncompute disabled (keeps ancilla qubits)
@qlassf(uncompute=False)
def fn(a: Qint[4]) -> bool:
    return a > 7

```

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

### Run Grover Search Simulation with Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_sat.ipynb

Runs the Grover search quantum circuit using qiskit's AerSimulator. Measures all qubits, transpile the circuit, executes the simulation, and retrieves the results. Decodes the counts to display a readable histogram. Requires importing QuantumCircuit, transpile, plot_histogram, and AerSimulator.

```python
from qiskit import QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
from qiskit_aer import AerSimulator

pc.measure_all()
simulator = AerSimulator()
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)

counts_readable = q_algo.decode_counts(counts, discard_lower=15)
plot_histogram(counts_readable)
```

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

### Compile the whole function with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/how_it_works.ipynb

Compiles the entire Python function into a single quantum circuit using qlasskit's integrated approach, resulting in a more optimized circuit.

```python
qc = QuantumCircuit(f_comp.num_qubits)
pc.append(f_comp.gate(), f_comp.qubits)
```

```python
print("Operations:", qc.decompose().count_ops())
```

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

### Parameter and UnboundQlassf.bind()

Source: https://context7.com/dakk/qlasskit/llms.txt

Allows for creating parameterized functions where arguments can be bound later. This results in an `UnboundQlassf` object that is compiled only after the `.bind()` method is called with concrete values, enabling circuit reuse.

```APIDOC
## `Parameter` and `UnboundQlassf.bind()` — Parameterized functions

Mark function arguments with `Parameter[T]` to defer binding. The result is an `UnboundQlassf` that is compiled only after `.bind()` is called with concrete values. This enables circuit reuse with different constant parameters without rewriting the function.

```python
from qlasskit import qlassf, Qint, Parameter

@qlassf
def threshold_check(limit: Parameter[Qint[4]], n: Qint[4]) -> bool:
    return n > limit

# Returns UnboundQlassf — not yet compiled
print(type(threshold_check))  # <class 'qlasskit.qlassfun.UnboundQlassf'>

# Bind the parameter to produce a compiled QlassF
check_gt5 = threshold_check.bind(limit=5)
check_gt10 = threshold_check.bind(limit=10)

print(check_gt5.num_qubits)
print(check_gt5.f()(Qint[4](7)))   # True
print(check_gt10.f()(Qint[4](7)))  # False
```
```

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

### DeutschJozsa Class Initialization

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.algorithms.deutschjozsa.DeutschJozsa.md

Initializes the DeutschJozsa algorithm with a given function.

```APIDOC
## DeutschJozsa(f: QlassF)

### Description
Initializes the DeutschJozsa algorithm with a function `f`.

### Parameters
#### Path Parameters
- **f** (QlassF) - Required - The function to be analyzed, which maps inputs to a boolean output.
```

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

### Export and Draw Oracle Circuit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover.ipynb

Export the compiled quantum circuit for the defined oracle function and draw it using Matplotlib. This step visualizes the quantum circuit generated by Qlasskit.

```python
and_all.export("qiskit").draw("mpl")
```

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

### Define Factorization Problem with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_grover_factors.ipynb

Defines a quantum function for factorization using qlasskit and initializes Grover's algorithm.

```python
from typing import Tuple
from qlasskit import qlassf, Qint
from qlasskit.algorithms import Grover


@qlassf
def factorize(a: Tuple[Qint[2], Qint[2]]) -> bool:
    return a[0] * a[1] == 9


q_algo = Grover(factorize)
```

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

### Use Grover's Algorithm with Qlasskit

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Utilize the Grover's algorithm implementation from Qlasskit to find inputs for which a given quantum function returns True. The circuit can be exported to various formats, such as Qiskit.

```python
from qlasskit.algorithms import Grover

algo = Grover(h, True)
pc = algo.circuit().export("circuit", "qiskit")
```

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

### Create and Optimize Boolean Function Circuit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/decompiler_and_optimizer.ipynb

Define a boolean function using qlassfa with fastOptimizer and generate its initial quantum circuit.

```python
from qlasskit import qlassfa, qlassf, boolopt, Qlist
from qlasskit.decompiler import Decompiler, circuit_boolean_optimizer


@qlassfa(bool_optimizer=boolopt.fastOptimizer)
def qf(a: Qlist[bool, 2]) -> bool:
    s = True
    for i in a:
        s = s and i
    return s


qf.circuit()
```

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

### Export Deutsch-Jozsa Quantum Circuit to Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_deutsch_jozsa.ipynb

Export the quantum circuit for the Deutsch-Jozsa algorithm to Qiskit format and draw it.

```python
qc = q_algo.export("qiskit")
pc.draw("mpl")
```

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

### qlasskit.bqm.decode_samples(qf, sampleset)

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.bqm.decode_samples.md

This function takes a quantum frustration (qf) object and a dimod sampleset as input. It processes the sampleset to return a high-level decoded solution.

```APIDOC
## qlasskit.bqm.decode_samples(qf, sampleset)

### Description
Get dimod sampleset and return an high level decoded solution.

### Parameters
#### Path Parameters
- **qf** (object) - Required - The quantum frustration object.
- **sampleset** (dimod.SampleSet) - Required - The input sampleset.

### Response
#### Success Response (object)
- Returns a high-level decoded solution.
```

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

### Create Quantum Circuit for qlassf Function

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/example_unitary_of_f.ipynb

Creates a qiskit QuantumCircuit from a qlassf function's gate and qubits. This is useful for further quantum operations.

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(f.num_qubits, f.num_qubits)
pc.append(f.gate(), f.qubits)

pc.save_state()
pc.decompose().draw("mpl")
```

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

### Export Quantum Circuit to Qiskit

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/quickstart.ipynb

Export the defined quantum function to the qiskit framework and draw the resulting circuit.

```python
circuit = sum_two_numbers.export("qiskit")
circuit.draw("mpl")
```

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

### Initialize Bernstein-Vazirani Algorithm

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/algorithms.ipynb

Construct a `BernsteinVazirani` algorithm instance using a secret oracle generated by `secret_oracle`. The `secret_oracle` function takes the number of bits and the secret value as arguments.

```python
from qlasskit.algorithms import BernsteinVazirani, secret_oracle

oracle = secret_oracle(4, 14)

q_algo = BernsteinVazirani(oracle)
```

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

### `QlassF.export()` / `.gate()` — Export to quantum framework

Source: https://context7.com/dakk/qlasskit/llms.txt

Export the compiled circuit to various quantum frameworks like Qiskit, Cirq, PennyLane, QASM, Sympy, or QuTiP. The export can be a full circuit or a reusable gate.

```APIDOC
## `QlassF.export()` / `.gate()` — Export to quantum framework

Export the compiled circuit to Qiskit, Cirq, PennyLane, QASM, Sympy, or QuTiP as a full circuit or as a reusable gate.

```python
from qlasskit import qlassf, Qint

@qlassf
def sum_two(a: Qint[2], b: Qint[2]) -> Qint[2]:
    return a + b

# Export as a Qiskit QuantumCircuit
qiskit_circ = sum_two.export("qiskit")
qiskit_circ.draw("mpl")

# Export as a Qiskit Gate (for embedding into larger circuits)
from qiskit import QuantumCircuit
from qlasskit import Qint2

pc = QuantumCircuit(sum_two.num_qubits, len(sum_two.output_qubits))
pc.initialize(sum_two.encode_input(Qint2(1), Qint2(2)), sum_two.input_qubits)
pc.append(sum_two.gate("qiskit"), sum_two.qubits)
pc.measure(sum_two.output_qubits, range(len(sum_two.output_qubits)))
```
```

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

### Decompiler Class Constructor

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/generated/qlasskit.decompiler.Decompiler.md

Initializes a new instance of the Decompiler class.

```APIDOC
## __init__()

### Description
Initializes a new instance of the Decompiler class.

### Method
__init__
```

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

### Quantum Hybrid Function

Source: https://github.com/dakk/qlasskit/blob/master/docs/source/supported.md

Demonstrates using a quantum gate (CX) within a Qlasskit function. Note that including quantum gates changes the function's behavior.

```python
def bell(a: bool, b: bool) -> bool:
   return Q.CX(Q.H(a), b)
```

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

### Use Helper Functions in Qlassf

Source: https://github.com/dakk/qlasskit/blob/master/README.md

Demonstrates how to use other Qlasskit-decorated functions within a new Qlasskit function. The `@qlassfa` decorator is used to provide definitions for helper functions.

```python
@qlassf
def equal_8(n: Qint[4]) -> bool:
  return equal_8 == 8

@qlassfa(defs=[equal_8])
def f(n: Qint[4]) -> bool:
  n = n+1 if equal_8(n) else n
  return n
```