Grover's algorithm break decrypt possibility using large scale distance ocean

 

import numpy as np

import matplotlib.pyplot as plt

# --- Logical error rate model (surface code threshold approximation) ---

def logical_error_rate(physical_error, threshold=0.01, code_distance=5):

    if physical_error >= threshold:

        return 0.5  # logical qubit fails

    return (physical_error / threshold) ** ((code_distance + 1) / 2)

# --- Channel model ---

def channel_error(distance_km, loss_db_per_km=0.2):

    loss_db = distance_km * loss_db_per_km

    transmission = 10 ** (-loss_db / 10)

    return 1 - transmission

# --- Repeater chain with QEC ---

def repeater_chain_fidelity(num_repeaters, segment_length_km, code_distance):

    physical_error = channel_error(segment_length_km)

    logical_error = logical_error_rate(physical_error, code_distance=code_distance)

    return (1 - logical_error) ** num_repeaters

# --- Grover success probability ---

def grover_success(fidelity):

    return fidelity ** 2

# --- Simulation ---

segment_length = 100  # km

repeaters = np.arange(1, 51)

code_distance = 7  # moderate surface code

fidelities = [repeater_chain_fidelity(n, segment_length, code_distance) for n in repeaters]

success = [grover_success(f) for f in fidelities]

plt.plot(repeaters, success)

plt.xlabel("Number of Repeaters (100 km spacing)")

plt.ylabel("Grover Success Probability")

plt.title("Grover Algorithm With Quantum Error Correction (Surface Code)")

plt.grid(True)

plt.show()