from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister

from qiskit.circuit.library import GroverOperator

from qiskit.algorithms import Grover

from qiskit.primitives import Sampler

import numpy as np

class DatabaseOracle:

def __init__(self, database_records, target_value, key_size):

"""

Initialize database oracle for Grover's algorithm

Args:

database_records (list): List of tuples (id, value) representing database

target_value: Value to search for

key_size (int): Number of qubits needed for surrogate key

"""

self.database = database_records

self.target = target_value

self.key_size = key_size

self.record_count = len(database_records)

def create_oracle_circuit(self) -> QuantumCircuit:

"""Create quantum circuit for database oracle"""

# Create quantum registers

qr_key = QuantumRegister(self.key_size, 'key')

qr_value = QuantumRegister(32, 'value') # Assuming 32-bit values

qr_ancilla = QuantumRegister(1, 'ancilla')

# Create quantum circuit

qc = QuantumCircuit(qr_key, qr_value, qr_ancilla)

# Implement database lookup

def database_lookup(qc, key_qubits, value_qubits):

"""

Implement reversible database lookup

Maps: |k⟩|0⟩ → |k⟩|v_k⟩ where v_k is the value for key k

"""

for record_id, value in self.database:

# Convert record_id to binary string

key_str = format(record_id, f'0{self.key_size}b')

# Control qubits for this record

ctrl_qubits = []

for i, bit in enumerate(key_str):

if bit == '1':

qc.x(key_qubits[i])

ctrl_qubits.append(key_qubits[i])

# Apply controlled-X gates to set value bits

value_str = format(value, '032b')

for i, bit in enumerate(value_str):

if bit == '1':

qc.mcx(ctrl_qubits, value_qubits[i])

# Uncompute key transformations

for i, bit in enumerate(key_str):

if bit == '1':

qc.x(key_qubits[i])

# Implement value comparison

def compare_value(qc, value_qubits, target_value, ancilla):

"""Compare value with target and set ancilla"""

# Convert target to binary

target_str = format(self.target, '032b')

# XOR value bits with target

for i, bit in enumerate(target_str):

if bit == '0':

qc.x(value_qubits[i])

# Multi-controlled NOT to ancilla

qc.mcx(value_qubits, ancilla)

# Uncompute XORs

for i, bit in enumerate(target_str):

if bit == '0':

qc.x(value_qubits[i])

# Implement full oracle

database_lookup(qc, qr_key, qr_value)

compare_value(qc, qr_value, self.target, qr_ancilla[0])

# Uncompute database lookup for reversibility

database_lookup(qc, qr_key, qr_value)

return qc

def grover_database_search(database_records, target_value, key_size):

"""

Perform Grover's search on database to find key for target value

Args:

database_records (list): List of (id, value) tuples

target_value: Value to search for

key_size (int): Number of bits in surrogate key

Returns:

int: Found key if successful

"""

# Create oracle

oracle = DatabaseOracle(database_records, target_value, key_size)

oracle_circuit = oracle.create_oracle_circuit()

# Create main circuit

qr_key = QuantumRegister(key_size, 'key')

cr_key = ClassicalRegister(key_size, 'output')

qc = QuantumCircuit(qr_key, cr_key)

# Initialize superposition

qc.h(qr_key)

# Calculate optimal number of iterations

n = key_size

N = 2**n

num_iterations = int(np.pi/4 * np.sqrt(N))

# Apply Grover iterations

for _ in range(num_iterations):

# Oracle

qc.compose(oracle_circuit, qubits=qr_key, inplace=True)

# Diffusion operator

qc.h(qr_key)

qc.x(qr_key)

qc.h(qr_key[-1])

qc.mcx(qr_key[:-1], qr_key[-1])

qc.h(qr_key[-1])

qc.x(qr_key)

qc.h(qr_key)

# Measure

qc.measure(qr_key, cr_key)

# Run on simulator

sampler = Sampler()

job = sampler.run(qc)

result = job.result()

# Process results

counts = result.quasi_dists[0]

most_frequent = max(counts.items(), key=lambda x: x[1])[0]

# Convert binary string to integer

found_key = int(most_frequent, 2)

# Verify result

for record_id, value in database_records:

if record_id == found_key and value == target_value:

return found_key

return None

# Example usage

def main():

# Example database with surrogate keys

database = [

(1, 42), # ID: 1, Value: 42

(2, 17), # ID: 2, Value: 17

(3, 73), # ID: 3, Value: 73

(4, 29), # ID: 4, Value: 29

(5, 55) # ID: 5, Value: 55

]

target_value = 73 # Value to search for

key_size = 3 # Enough bits to represent all IDs

print(f"Searching for record with value: {target_value}")

print(f"Database size: {len(database)} records")

print(f"Key size: {key_size} bits")

# Run Grover's algorithm

result = grover_database_search(database, target_value, key_size)

if result:

print(f"Found record with ID: {result}")

else:

print("Record not found")

if __name__ == "__main__":

main()