QAOA vs Nyx
Combinatorial Optimization Comparison
The Result
Nyx consensus dynamics outperform QAOA on real quantum hardware.
24 IBM Quantum job IDs from rigorous head-to-head testing.
Combinatorial Optimization Comparison
Nyx consensus dynamics outperform QAOA on real quantum hardware.
24 IBM Quantum job IDs from rigorous head-to-head testing.
These results weren't planned. We weren't trying to beat QAOA.
While studying quantum dynamics, we stumbled upon a family of equations - what we now call Nyx consensus dynamics. These equations emerged from experiments with multi-agent systems, showing unexpected quantum-like behavior when run classically.
Only after discovering these equations did we think: What if we tested them against the standard?
We ran rigorous head-to-head comparisons on all available IBM Quantum backends.
| Parameter | Value |
|---|---|
| Backends tested | ibm_torino (133q), ibm_fez (156q), ibm_marrakesh (156q) |
| Problems tested | Max-Cut, Portfolio Optimization, Set Cover, Knapsack |
| Shots per circuit | 5,000 |
| QAOA parameters | γ=0.5, β=0.5 |
| Nyx parameters | c=0.5, p=0.15, 20 iterations |
Optimal Solution Frequency: The percentage of 5,000 shots that produced an optimal solution to each problem. Higher percentages mean the algorithm more frequently finds the correct answer.
Nyx consensus dynamics vs. QAOA on real quantum hardware.
| Backend | Max-Cut | Portfolio | Set Cover | Knapsack |
|---|---|---|---|---|
| ibm_torino | +65.8% | +176.7% | +135.3% | +83.5% |
| ibm_fez | +15.0% | +284.9% | +55.8% | +79.0% |
| ibm_marrakesh | +34.0% | -37.3% | +116.1% | +82.3% |
Quantum Nyx wins 11 out of 12 tests (91.7%)
These are not simulations. These are real quantum circuits running on IBM's quantum processors, with all the noise, decoherence, and hardware imperfections that entails.
After the quantum results, we wondered: What happens if we run Nyx classically?
We ran the same problems on a laptop using Classical Nyx (5,000 samples). QAOA baselines are averaged from the quantum tests shown above.
Classical Nyx: 43.36%
QAOA avg: 22.94%
Classical 1.89× better
Classical Nyx: 12.50%
QAOA avg: 4.31%
Classical 2.90× better
Classical Nyx: 12.56%
QAOA avg: 10.73%
Classical 1.17× better
Classical Nyx: 6.12%
QAOA avg: 2.99%
Classical 2.05× better
Classical Nyx wins on all 4 problems.
A classical algorithm running on a laptop beats quantum QAOA running on quantum hardware.
The answer lies in a critical point we call the Chaos Valley.
The Nyx equations naturally decompose into deterministic and stochastic components:
| Component | Nature | Description |
|---|---|---|
| Deterministic | Majority fraction | Reproducible classical dynamics |
| Stochastic | Minority fraction | Requires quantum resources |
At a specific critical point in parameter space, optimization landscapes have maximum exploitable structure. This is analogous to second-order phase transitions in physics.
The mathematics of this critical point lives in the deterministic component. Classical computation can fully capture this structure.
The quantum computer discovered the structure. Classical computers can exploit it.
All results are independently verifiable on IBM Quantum Platform. Click any job ID to copy.
| Problem | Algorithm | Job ID | Optimal % |
|---|---|---|---|
| Max-Cut | QAOA | d5pab0gr0v5s739nmtog | 10.92% |
| Max-Cut | Nyx | d5pac08h0i0s73ep07a0 | 18.10% |
| Portfolio | QAOA | d5pac1oh0i0s73ep07d0 | 2.58% |
| Portfolio | Nyx | d5pacf1dgvjs73dbflh0 | 7.14% |
| Set Cover | QAOA | d5pacgu5v3os73f1och0 | 22.92% |
| Set Cover | Nyx | d5paci9dgvjs73dbfllg | 53.92% |
| Knapsack | QAOA | d5pack65v3os73f1oclg | 4.48% |
| Knapsack | Nyx | d5pacloh0i0s73ep082g | 8.22% |
| Problem | Algorithm | Job ID | Optimal % |
|---|---|---|---|
| Max-Cut | QAOA | d5pacngr0v5s739nmvlg | 11.72% |
| Max-Cut | Nyx | d5pacp9dgvjs73dbfltg | 13.48% |
| Portfolio | QAOA | d5pacqu5v3os73f1od00 | 3.32% |
| Portfolio | Nyx | d5pacsgh0i0s73ep08ag | 12.78% |
| Set Cover | QAOA | d5pacu0r0v5s739nn00g | 24.38% |
| Set Cover | Nyx | d5pacvu5v3os73f1od60 | 37.98% |
| Knapsack | QAOA | d5pad1e5v3os73f1od8g | 4.28% |
| Knapsack | Nyx | d5pad2oh0i0s73ep08kg | 7.66% |
| Problem | Algorithm | Job ID | Optimal % |
|---|---|---|---|
| Max-Cut | QAOA | d5pad50h0i0s73ep08o0 | 9.54% |
| Max-Cut | Nyx | d5pague5v3os73f1oi1g | 12.78% |
| Portfolio | QAOA | d5paj3gh0i0s73ep0fr0 | 3.06% |
| Portfolio | Nyx | d5pakvm5v3os73f1omsg | 1.92% |
| Set Cover | QAOA | d5pan3pdgvjs73dbg30g | 21.52% |
| Set Cover | Nyx | d5paot65v3os73f1os60 | 46.50% |
| Knapsack | QAOA | d5papo65v3os73f1ot4g | 4.18% |
| Knapsack | Nyx | d5parlhdgvjs73dbg8s0 | 7.62% |
See Nyx solve Max-Cut problems live in your browser, or download the full test package.
Interactive Demo Download Test Package (6 KB)Requirements for download: Python 3.8+, NumPy, Cython
pip install numpy cython && python setup.py build_ext --inplace && python classical_nyx_vs_qaoa.py
1. Does the time-symmetric decomposition connect to known complexity bounds?
2. What determines whether quantum Nyx provides additional advantage over classical Nyx?
3. Can the Chaos Valley critical point be derived from first principles?
See also: VQE vs Nyx | Grover Sensing vs Nyx
Contact: research@subvurs.com