DOI: 10.5281/zenodo.16870226
title: Structured Collapse for the Traveling Salesman Problem via QIRT on Real Quantum Hardware

description: 6-City Traveling Salesman Problem (TSP) - Quantum Circuit Results

Paper: Adaptive Quantum Circuit Architecture for Combinatorial OptimizationAuthors: Kristopher Knudsen, Axion MetricsHardware: IBM Brisbane (127-qubit QPU)Date: August 2025

Dataset Overview

This dataset contains 8,092 quantum measurements from a 6-city Traveling Salesman Problem solved using Adaptive Quantum Circuit Architecture (AQC) with Meta-Floor feedback systems. Each measurement represents a 12-bit quantum state collapse that encodes a potential TSP tour solution.

Key Results:



616 valid tours identified from 8,092 total measurements

7.61% success rate for valid TSP solutions

37 unique valid tour sequences discovered

First demonstration of symbolic collapse shaping for TSP constraints on quantum hardware


File Contents



job-d2ecpif36hfc738r1bgg-result.json - Raw quantum measurement data (8,092 samples)


Data Encoding Scheme

Bit Layout (12 measured bits per shot)

Bit positions:  11 10  9  8  7  6  5  4  3  2  1  0
               [AN][AN][-------- TOUR CODE ---------]




Bits 0-9 (LSB): 10-bit Lehmer/factoradic code encoding a 6-city permutation

Bits 10-11: Ancilla flags from Meta-Floor drift/reset monitors

Little-endian format: Bit 0 = least significant bit


Decoding Process

Step 1: Extract Components

x = int(hex_string, 16)          # Convert hex to integer
tour_code = x & 0x3FF            # Extract bits 0-9 (tour code)  
ancilla_flags = (x >> 10) & 0x3  # Extract bits 10-11 (ancilla)


Step 2: Validate Tour Code

if tour_code < 720:  # 6! = 720 valid permutations
    # Valid tour - proceed to decode
else:
    # Invalid - tour code overflow


Step 3: Lehmer/Factoradic Decode

def lehmer_to_permutation(tour_code):
    cities = [0, 1, 2, 3, 4, 5]
    permutation = []
    value = tour_code
    
    # Factoradic decode with radices [6,5,4,3,2,1]
    for k in [6, 5, 4, 3, 2, 1]:
        digit = value % k
        value = value // k
        permutation.append(cities.pop(digit))
    
    return permutation


Step 4: Canonicalize Tour

def canonicalize_tour(tour):
    # Rotate so city 0 appears first (removes rotational symmetry)
    zero_index = tour.index(0)
    return tour[zero_index:] + tour[:zero_index]


Worked Examples

Example 1: Valid Tour

Hex: 0x63e
Integer: 1598
Binary: 011000111110
Tour code: 574 (bits 0-9)
Ancilla: 1 (bits 10-11)
Status: VALID (574 < 720)
Decoded tour: [4,0,5,2,3,1]
Canonical tour: [0,5,2,3,1,4]


Example 2: Invalid Tour

Hex: 0xb99  
Integer: 2969
Binary: 101110011001
Tour code: 921 (bits 0-9)
Ancilla: 2 (bits 10-11)  
Status: INVALID (921 >= 720)


Example 3: Clean Valid Tour

Hex: 0x79
Integer: 121
Binary: 000001111001
Tour code: 121 (bits 0-9)
Ancilla: 0 (bits 10-11)
Status: VALID + CLEAN (no ancilla flags)
Decoded tour: [1,0,2,4,3,5]
Canonical tour: [0,2,4,3,5,1]


Analysis Categories

All Valid Tours



Criteria: tour_code < 720

Expected rate: ~70% (theoretical uniform distribution)

Actual rate: Varies by sample analysis


Clean Valid Tours



Criteria: tour_code < 720 AND ancilla_flags == 0

Description: Tours generated without Meta-Floor corrections

Significance: Represents cleanest quantum evolution


Paper Success Rate (7.61%)



Criteria: Clean valid tours meeting additional optimization constraints

Count: 616 out of 8,092 total measurements

Significance: High-quality TSP solutions via quantum entropy guidance


Quick Validation Code

import json

# Load dataset
with open('job-d2ecpif36hfc738r1bgg-result.json', 'r') as f:
    data = json.load(f)

samples = data['results'][0]['data']['ce']['samples']
print(f"Total measurements: {len(samples)}")

# Validate first few samples
for i, hex_str in enumerate(samples[:5]):
    x = int(hex_str, 16)
    tour_code = x & 0x3FF
    ancilla = (x >> 10) & 0x3
    valid = tour_code < 720
    
    print(f"{hex_str}: code={tour_code}, ancilla={ancilla}, valid={valid}")


 

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