Structured Collapse for the Traveling Salesman Problem via QIRT on Real Quantum Hardware

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}") © 2025 Axion Metrics LLC. All rights reserved.This work is protected under U.S. copyright law. Redistribution or reproduction of this dataset or its components, in whole or in part, is prohibited without explicit written permission from the copyright holder, except for non-commercial academic or research use. Researchers are permitted to analyze, cite, and build upon this work for scholarly purposes, provided appropriate attribution is given.For all commercial uses, redistribution, or integration into other software platforms, written authorization is required.