Quantum Distance Superposition: The Code - A simplifed model for Infinite-Route AI Optimization
Below is one way to implement a “distance superposition†approach in a computational algorithm. The idea is to treat every possible route between two nodes as a candidate “state†in a superposition. Rather than exhaustively evaluating every infinite possibility (which is impossible in practice), we use a Monte Carlo–style sampling to generate many random paths. Each path is assigned a weight (or amplitude) that decreases with its “action†(here taken as the cumulative distance or cost). The superposition is then “collapsed†by selecting the path with the highest amplitude (or equivalently the lowest cost), which is analogous to the quantum collapse described in the article.
The original article for reference: The Superposition of Distance: A Quantum-Relativistic Paradigm of Finite Points in Infinite Space
Below is the pseudocode outline and a Python implementation using a sample graph (built with NetworkX):
Algorithm Outline: Distance Superposition Monte Carlo (DSMC)
- Input: ? A graph GG with nodes and weighted edges (representing distances). ? A starting node SS and an ending node TT. ? Parameters: number of samples NN, maximum steps per random walk, and a “temperature†parameter that controls the weighting (akin to a quantum action scale).
- Path Sampling: ? For each sample (up to NN): Generate a random path (using a constrained random walk) from SS to TT. If the path reaches TT within the maximum steps, compute its total cost. Compute the “amplitude†for the path using a Boltzmann-like factor, e.g., amplitude=e?cost/T\text{amplitude} = e^{-\text{cost}/T} where TT is the temperature parameter.
- Superposition and Collapse: ? Normalize the amplitudes to create a probability distribution over all sampled paths. ? Either select the path with the maximum amplitude (lowest cost) or sample according to the computed probabilities—this is the “collapse†to a definite distance.
- Output: ? Return the selected (optimal) path and its cost.
Python Code Example
import networkx as nx
import random
import math
import numpy as np
def sample_random_path(G, start, end, max_steps):
"""
Generates a random path from start to end using a random walk,
constrained to a maximum number of steps.
"""
current = start
path = [current]
steps = 0
while current != end and steps < max_steps:
neighbors = list(G.neighbors(current))
if not neighbors:
break # Dead end
# Randomly choose the next node
next_node = random.choice(neighbors)
path.append(next_node)
current = next_node
steps += 1
return path if current == end else None
def path_cost(G, path):
"""
Computes the total cost (distance) of a given path.
"""
cost = 0
for i in range(len(path) - 1):
# Use the 'weight' attribute; default to 1 if not present
cost += G[path[i]][path[i+1]].get('weight', 1)
return cost
def distance_superposition_search(G, start, end, num_samples=1000, max_steps=50, temperature=1.0):
"""
Samples many possible paths from start to end.
Each path's amplitude is computed based on its cost.
The superposition of these amplitudes is used to "collapse" to an optimal path.
"""
sampled_paths = []
amplitudes = []
for in range(numsamples):
path = sample_random_path(G, start, end, max_steps)
if path is None:
continue # Skip if destination not reached
cost = path_cost(G, path)
# Compute amplitude using an exponential decay (lower cost yields higher amplitude)
amplitude = math.exp(-cost / temperature)
sampled_paths.append((path, cost, amplitude))
amplitudes.append(amplitude)
if not sampled_paths:
return None, None # No valid paths found
# Normalize amplitudes to create a probability distribution
total_amp = sum(amplitudes)
probabilities = [amp / total_amp for amp in amplitudes]
# Option 1: Select the best path (maximum amplitude, i.e. lowest cost)
best_index = np.argmax(amplitudes)
best_path, best_cost, = sampledpaths[best_index]
# Option 2 (alternative): Randomly select a path weighted by its probability
# chosen_index = np.random.choice(len(sampled_paths), p=probabilities)
# chosen_path, chosen_cost, = sampledpaths[chosen_index]
# For demonstration, we return the best (optimal) path
return best_path, best_cost
def main():
# Create a sample 2D grid graph
G = nx.grid_2d_graph(5, 5) # 5x5 grid where nodes are labeled as (x, y) tuples
# Assign random weights to each edge to simulate variable distances
for (u, v) in G.edges():
G[u][v]['weight'] = random.uniform(1, 10)
start = (0, 0)
end = (4, 4)
best_path, best_cost = distance_superposition_search(G, start, end,
num_samples=10000,
max_steps=20,
temperature=1.0)
if best_path is not None:
print("Best path found:", best_path)
print("Total cost:", best_cost)
else:
print("No valid path found between", start, "and", end)
if name == "__main__":
main()
Explanation
- Random Path Sampling: The function sample_random_path performs a constrained random walk from the starting node to the target node. Not every sample will reach the destination, so those that don’t are discarded.
- Amplitude Calculation: For each successful path, the total cost is computed. An amplitude is calculated using an exponential decay factor so that paths with lower cost (i.e., more optimal routes) have higher amplitudes.
- Superposition & Selection: The algorithm “superposes†all the candidate paths by considering their amplitudes and then “collapses†this superposition by selecting the path with the highest amplitude (or using a probability distribution derived from these amplitudes). This simulates the idea that before measurement (or selection), the system exists in a superposition of infinite possible routes, and only upon selection does a finite (optimal) distance emerge.
- Parameters: The temperature parameter plays a role analogous to that in simulated annealing; it controls how strongly cost differences affect the amplitude. The higher the temperature, the more uniform the amplitudes will be, allowing exploration of more paths.
This code implements a simplified version of the “distance superposition†concept inspired by the article “The Superposition of Distance: A Quantum-Relativistic Paradigm of Finite Points in Infinite Space†by Ian Kano. In a practical AI application—such as route optimization or path planning in robotics or network routing—this kind of probabilistic, sampling-based approach can help explore a vast number of possibilities quickly and converge on an optimal solution.
Feel free to modify the parameters or integrate more sophisticated path sampling (or even quantum-inspired optimization techniques) depending on the specific application and performance requirements.
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