BB84 QKD algorithm (#7898)

* Added BB84 algorithm.

* Function name lowercase + imports fix

I thought uppercase was appropriate because they're initials.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update quantum/bb84.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Removed python < 3.11 restriction from qiskit

* Removed python < 3.11 restriction from qiskit

* scikit-learn

* Update quantum/bb84.py

Correct typo in `default_rng()` call

Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

quantum/bb84.py

@@ -0,0 +1,133 @@
+#!/usr/bin/env python3
+"""
+Simulation of the Quantum Key Distribution (QKD) protocol called BB84,
+created by Charles Bennett and Gilles Brassard in 1984.
+
+BB84 is a key-distribution protocol that ensures secure key distribution
+using qubits instead of classical bits. The generated key is the result
+of simulating a quantum circuit. Our algorithm to construct the circuit
+is as follows:
+
+Alice generates two binary strings. One encodes the basis for each qubit:
+
+ - 0 -> {0,1} basis.
+ - 1 -> {+,-} basis.
+
+The other encodes the state:
+
+ - 0 -> |0> or |+>.
+ - 1 -> |1> or |->.
+
+Bob also generates a binary string and uses the same convention to choose
+a basis for measurement. Based on the following results, we follow the
+algorithm below:
+
+X|0> = |1>
+
+H|0> = |+>
+
+HX|0> = |->
+
+1. Whenever Alice wants to encode 1 in a qubit, she applies an
+X (NOT) gate to the qubit. To encode 0, no action is needed.
+
+2. Wherever she wants to encode it in the {+,-} basis, she applies
+an H (Hadamard) gate. No action is necessary to encode a qubit in
+the {0,1} basis.
+
+3. She then sends the qubits to Bob (symbolically represented in
+this circuit using wires).
+
+4. Bob measures the qubits according to his binary string for
+measurement. To measure a qubit in the {+,-} basis, he applies
+an H gate to the corresponding qubit and then performs a measurement.
+
+References:
+https://en.wikipedia.org/wiki/BB84
+https://qiskit.org/textbook/ch-algorithms/quantum-key-distribution.html
+"""
+import numpy as np
+import qiskit
+
+
+def bb84(key_len: int = 8, seed: int | None = None) -> str:
+    """
+    Performs the BB84 protocol using a key made of `key_len` bits.
+    The two parties in the key distribution are called Alice and Bob.
+    Args:
+        key_len: The length of the generated key in bits. The default is 8.
+
+        seed: Seed for the random number generator.
+        Mostly used for testing. Default is None.
+
+    Returns:
+        key: The key generated using BB84 protocol.
+
+    >>> bb84(16, seed=0)
+    '1101101100010000'
+
+    >>> bb84(8, seed=0)
+    '01011011'
+    """
+    # Set up the random number generator.
+    rng = np.random.default_rng(seed=seed)
+
+    # Roughly 25% of the qubits will contribute to the key.
+    # So we take more than we need.
+    num_qubits = 6 * key_len
+    # Measurement basis for Alice's qubits.
+    alice_basis = rng.integers(2, size=num_qubits)
+    # The set of states Alice will prepare.
+    alice_state = rng.integers(2, size=num_qubits)
+    # Measurement basis for Bob's qubits.
+    bob_basis = rng.integers(2, size=num_qubits)
+
+    # Quantum Circuit to simulate BB84
+    bb84_circ = qiskit.QuantumCircuit(num_qubits, name="BB84")
+
+    # Alice prepares her qubits according to rules above.
+    for index, _ in enumerate(alice_basis):
+        if alice_state[index] == 1:
+            bb84_circ.x(index)
+        if alice_basis[index] == 1:
+            bb84_circ.h(index)
+    bb84_circ.barrier()
+
+    # Bob measures the received qubits according to rules above.
+    for index, _ in enumerate(bob_basis):
+        if bob_basis[index] == 1:
+            bb84_circ.h(index)
+
+    bb84_circ.barrier()
+    bb84_circ.measure_all()
+
+    # Simulate the quantum circuit.
+    sim = qiskit.Aer.get_backend("aer_simulator")
+    # We only need to run one shot because the key is unique.
+    # Multiple shots will produce the same key.
+    job = qiskit.execute(bb84_circ, sim, shots=1, seed_simulator=seed)
+    # Returns the result of measurement.
+    result = job.result().get_counts(bb84_circ).most_frequent()
+
+    # Extracting the generated key from the simulation results.
+    # Only keep measurement results where Alice and Bob chose the same basis.
+    gen_key = "".join(
+        [
+            result_bit
+            for alice_basis_bit, bob_basis_bit, result_bit in zip(
+                alice_basis, bob_basis, result
+            )
+            if alice_basis_bit == bob_basis_bit
+        ]
+    )
+
+    # Get final key. Pad with 0 if too short, otherwise truncate.
+    key = gen_key[:key_len] if len(gen_key) >= key_len else gen_key.ljust(key_len, "0")
+    return key
+
+
+if __name__ == "__main__":
+    print(f"The generated key is : {bb84(8, seed=0)}")
+    from doctest import testmod
+
+    testmod()

requirements.txt

@@ -8,11 +8,11 @@ opencv-python
 pandas
 pillow
 projectq
-qiskit; python_version < "3.11"
+qiskit
 requests
 rich
 scikit-fuzzy
-sklearn
+scikit-learn
 statsmodels
 sympy
 tensorflow; python_version < "3.11"