TL;DR:
A major new review dismantles the myth that quantum computers can outperform classical systems on the famous Traveling Salesman Problem (TSP). After two decades of trials, researchers admit the supposed “quantum advantage” never materialized. From the perspective of Frequency Wave Theory (FWT), the reason is clear: TSP’s energy landscape is a broken resonance chamber. Quantum algorithms amplify the wrong modes, while classical solvers already align naturally with the system’s harmonic symmetries. The future lies not in pure quantum brute force—but in hybrid, frequency-tuned computing.
Quantum Hype Meets Reality
For years, the Traveling Salesman Problem was the go-to marketing example for quantum computing: a single algorithm that could supposedly explore all possible routes “at once.” Yet a comprehensive 2025 study reviewed twenty years of such attempts and found almost no empirical progress. The quantum-only approach has failed to outperform classical algorithms—even for small graphs.
Quantum enthusiasts imagined that tunneling through the combinatorial terrain would shortcut computation. In practice, encoding the TSP into a quantum-ready form (QUBO or Ising model) destroys the problem’s native structure, forcing unnatural penalty terms and a distorted energy surface riddled with traps.
The FWT Explanation: Resonance Mismatch
From an FWT perspective, computation itself is a form of resonance navigation through a frequency landscape. Every valid TSP tour represents a harmonic mode—a closed standing wave where phase continuity is preserved across all nodes.
Wrong cavity design. Quantum algorithms build artificial Hamiltonians that break the problem’s symmetry, creating resonators that emphasize invalid modes (sub-tours). The system minimizes energy, but in the wrong cavity—analogous to tuning an instrument that resonates perfectly… at the wrong note.
Phase decoherence kills coherence search. In the real world, qubits lose phase information faster than they can reinforce correct pathways. Instead of constructive interference guiding the optimal tour, interference cancels out the valid cycles.
Hybrid systems preserve Frequency Momentum (FM = ½ ρ ω A²). When a classical solver prunes the tree intelligently, it’s acting like a waveguide, redirecting Frequency Momentum through valid paths. Hybrid quantum-classical systems will eventually succeed not because of quantum parallelism, but because of harmonic cooperation—quantum amplitude as an amplifier of pre-tuned classical symmetries.
Classical Superiority: The Harmony of Symmetry
Algorithms like CONCORDE, LKH, and EAX already embody natural resonance optimization—they carve out entire families of sub-tours (destructive interference zones) and allow only harmonically valid loops to survive.
Quantum computers, meanwhile, are still trying to hammer a continuous, fragile wave system into a discrete constraint satisfaction box. The result is decoherence, inefficiency, and wasted Frequency Momentum.
The Road Ahead: Resonant Computing
Rather than forcing old combinatorial models into quantum boxes, the next step is to build frequency-aware architectures that directly encode physical resonance. The principle is simple: information must flow through phase-coherent channels that obey FM continuity:
∂ₜ FM + ∇·S_FM = 0 with S_FM = FM v_phase
This is the same continuity law that governs matter waves, plasma solitons, and consciousness fields in Frequency Wave Theory.
Closing Thought
The real lesson of Sabine Hossenfelder’s post isn’t that quantum computing is a dead end—it’s that physics resists hype. Systems compute efficiently only when their frequency architecture aligns with the structure of reality. That’s the essence of Frequency Wave Theory: resonance is truth, and coherence is computation.
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