QWO: Quantum Wavefunction Optimizer

A simulator-based research prototype of a distribution-based global optimizer over a discretised parameter grid. It maintains a complex amplitude over candidate parameters, lets the loss landscape shape that amplitude through a loss-dependent phase and a mixing step, samples candidates from the induced probability, and refines the best ones with a classical local search. It is benchmarked against classical optimizers on synthetic landscapes.

Simulator-based research prototype. No quantum-advantage claim.

Core idea

• Keep a complex amplitude $\psi(\theta)$ over a grid of candidate parameters $\theta$.
• The probability of sampling a candidate is $|\psi(\theta)|^2$.
• Apply a loss-dependent phase (low-loss regions accumulate weight), then a mixing / diffusion step, then renormalize.
• Sample candidates from the distribution and refine them with a classical local optimizer; compare against classical optimizers under a matched evaluation budget.

Mathematical sketch

Represent a probability over the parameter grid as the normalized squared modulus of a complex amplitude:

$$p_t(\theta) = \frac{|\psi_t(\theta)|^{2}}{\sum_{\theta'} |\psi_t(\theta')|^{2}}.$$

Each step applies a loss-dependent phase and a mixing operator $M$, then renormalizes:

$$\psi_{t+1}(\theta) \;\propto\; M\!\left[\, e^{-\,i\,\eta\,L(\theta)}\,\psi_t(\theta) \,\right],$$

after which candidate solutions are drawn $\theta \sim p_t(\theta)$ and refined by a classical local optimizer.

Selected visuals and results

Exploratory outcome tally across synthetic landscapes (lower loss is better). Classical baselines win or tie on most tasks — an honest, mixed result.

Selected synthetic optimization landscapes.

How to run

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

python scripts/run_all_experiments.py --quick
pytest -q

Results status

• Exploratory, simulator-based, small grids.
• Honest outcome: on the tested synthetic landscapes, classical baselines win or tie on most tasks; the prototype leads on a few.
• Much of the prototype's measured success comes from the classical local-refinement step rather than from the amplitude dynamics.
• No quantum advantage is claimed. No state-of-the-art claim is made.

Limitations

• A complex array over a discretised grid; small dimension — classically tractable.
• Heuristic schedules (step sizes, sample counts) are fixed defaults.
• No hardware noise model.
• Classical optimizers often match or outperform the prototype here.