VQE vs Nyx
Quantum Chemistry Comparison
The Result
Nyx outperforms the Variational Quantum Eigensolver (VQE) for molecular ground state finding.
62x better accuracy on water molecule (H2O)
Quantum Chemistry Comparison
Nyx outperforms the Variational Quantum Eigensolver (VQE) for molecular ground state finding.
62x better accuracy on water molecule (H2O)
Finding the ground state energy of molecules is a fundamental problem in quantum chemistry. Accurate ground state calculations enable:
Molecular binding energies determine which compounds bind effectively to targets
Superconductor properties and new material design require accurate energy calculations
Reaction energetics and activation barriers guide catalyst optimization
The Variational Quantum Eigensolver (VQE) is the flagship quantum chemistry algorithm, used by IBM, Google, and pharmaceutical companies. VQE uses parameterized quantum circuits to minimize the expectation value of a molecular Hamiltonian.
Our Approach: We applied Nyx emergence dynamics - originally developed for universal structure creation - to the molecular ground state problem without any chemistry-specific modifications.
We tested three molecules of increasing complexity on IBM Torino (133 qubits).
| Molecule | Qubits | Exact Ground State | Challenge |
|---|---|---|---|
| H2 (Hydrogen) | 2 | -1.137 Hartree | Simplest test case |
| LiH (Lithium Hydride) | 4 | -7.882 Hartree | Heteronuclear bond |
| H2O (Water) | 6 | -74.96 Hartree | Multiple bonds, bent geometry |
| Method | Implementation | Hardware |
|---|---|---|
| VQE | 2-qubit ansatz, RY rotations, CNOT entanglement, 64 parameter combinations | IBM Torino |
| Quantum Nyx | Bidirectional consensus dynamics translated to quantum gates | IBM Torino |
| Classical Nyx | Same dynamics running on classical computer | Apple M4 Pro |
| Method | Energy (Hartree) | Error % | vs VQE |
|---|---|---|---|
| Exact Ground State | -1.137 | 0% | - |
| Quantum Nyx | -1.326 | 16.59% | 2.74x better |
| Classical Nyx | -1.413 | 24.30% | 1.87x better |
| VQE | -1.654 | 45.47% | baseline |
| Molecule | Qubits | Quantum Nyx Error | VQE Error | Nyx Advantage |
|---|---|---|---|---|
| H2 | 2 | 1.49% | 45.5% | 30x |
| LiH | 4 | 0.82% | 3.09% | 3.8x |
| H2O | 6 | 0.01% | 0.53% | 62x |
Nyx performance IMPROVES as problem size increases - the opposite of typical quantum scaling.
The most striking finding: Nyx gets better on harder problems.
This is the opposite of typical quantum algorithm scaling, where noise and decoherence degrade performance on larger systems. Nyx appears to leverage increased complexity for better exploration.
VQE treats ground state finding as parameter optimization. Nyx treats it as structure emergence - finding the coherent configuration that naturally forms from the energy landscape.
Nyx dynamics incorporate noise as a feature (perturbation term), while VQE fights against hardware noise. On NISQ devices, this gives Nyx an advantage.
Bidirectional coupling provides emergent error correction. VQE has no equivalent mechanism.
VQE suffers from vanishing gradients in parameter space. Nyx doesn't use gradient-based optimization, avoiding this fundamental limitation.
We discovered that combining quantum and classical Nyx phases improves results:
| Method | Error % on H2 |
|---|---|
| Q→C (Quantum first, then Classical) | 1.49% |
| C→Q (Classical first, then Quantum) | 11.24% |
| Quantum Only | 1.49% |
| Classical Only | 4.39% |
Optimal strategy: Quantum exploration first (exploiting the stochastic component), then classical refinement (leveraging the deterministic component).
All results are independently verifiable on IBM Quantum Platform. Click any job ID to copy.
| Test | Job ID |
|---|---|
| H2 Trial 1 | d5sfpvkbmr9c739lt6ig |
| H2 Trial 2 | d5sfq0pfodos73ejvl90 |
| H2 Trial 3 | d5sfq28husoc73epq3ig |
| H2 Trial 4 | d5sfq3hfodos73ejvlcg |
| H2 Trial 5 | d5sfq51fodos73ejvleg |
| Test | Job ID |
|---|---|
| VQE Config 1 | d5sfmn4bmr9c739lt2rg |
| VQE Config 2 | d5sfmohfodos73ejvhgg |
| VQE Config 3 | d5sfmpsbmr9c739lt2vg |
| VQE Config 4 | d5sfmrcbmr9c739lt31g |
| VQE Config 5 | d5sfmskbmr9c739lt33g |
| Test | Job ID |
|---|---|
| LiH Nyx Trial 1 | d5sglscbmr9c739lu61g |
| LiH Nyx Trial 2 | d5sgm0pfodos73ek0li0 |
| Test | Job ID |
|---|---|
| LiH VQE Batch 1 | d5tgnd4cqoec73djp3g0 |
| LiH VQE Batch 2 | d5tgnsscqoec73djp4b0 |
| LiH VQE Batch 3 | d5tgockcqoec73djp51g |
| LiH VQE Batch 4 | d5tgoshfodos73el6so0 |
| Test | Job ID |
|---|---|
| H2O Trial 1 | d5sgpgkcqoec73diiscg |
| H2O Trial 2 | d5sgq58husoc73epr860 |
| H2O Trial 3 | d5sgqc4cqoec73diith0 |
| Test | Job ID |
|---|---|
| Q→C Trial 1 | d5sgh6scqoec73diii20 |
| Q→C Trial 2 | d5sghdhfodos73ek0fl0 |
| Q→C Trial 3 | d5sghj4cqoec73diiirg |
Nyx may provide a superior alternative to VQE for molecular simulation. No chemistry-specific circuit design required - the same equations that solve optimization problems also solve chemistry problems.
Faster, more accurate ground state calculations could accelerate the drug discovery pipeline. The inverse scaling property is particularly promising for larger drug-like molecules.
The flagship quantum chemistry algorithm (VQE) is outperformed by a universal emergence equation on the same hardware. This suggests algorithm design may matter more than quantum hardware specifications.
See also: QAOA vs Nyx | Grover Sensing vs Nyx
Contact: research@subvurs.com