QIFM: Quantum Interference Field Machine

A simulator-based research prototype of a continuous-time, complex-state classifier inspired by quantum dynamics. Instead of stacked affine layers and pointwise nonlinearities, an input is encoded into a complex state that evolves under a small trainable generator; class scores are read out from several snapshots in time. It is benchmarked against classical baselines at matched data and parameter budgets.

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

Core idea

• Encode an input $x$ into an initial complex state.
• Evolve it continuously in time under a small, trainable generator.
• Read out class scores from a few time snapshots via trainable projectors.
• Train all continuous parameters end-to-end by cross-entropy, and compare with classical baselines (logistic regression, a tiny MLP, RBF SVM, random Fourier features) at the same data and parameter budget.

Mathematical sketch

Encode the input, then evolve the state continuously under a trainable generator $H_\theta$:

$$|\psi_0(x)\rangle = E_\theta(x), \qquad |\psi(t)\rangle = e^{-\,i\,t\,H_\theta}\,|\psi_0(x)\rangle.$$

Combine $K$ snapshot times ${t_1,\dots,t_K}$ into class scores and normalize:

$$s_c(x) = \sum_{k=1}^{K} w_{k,c}\, \langle \psi(t_k)\,|\,\Pi_c\,|\,\psi(t_k)\rangle, \qquad p(y=c\,|\,x) = \operatorname{softmax}_c\, s_c(x).$$

The forward map is norm-preserving (the evolution is unitary), so the model's nonlinearity comes from the multi-snapshot read-out rather than from pointwise activation functions.

Selected visuals and results

Exploratory matched-budget comparison on toy classification tasks. Each point is one task; the dashed line is parity. Results are mixed.

Selected toy datasets used for the exploration.

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 scale (small state dimension).
• Results are mixed across the toy tasks; classical baselines match or exceed the prototype on a number of them.
• No quantum advantage is claimed. No state-of-the-art claim is made.

Limitations

• NumPy / SciPy simulator only; small state dimension — classically tractable.
• Tiny optimizer (L-BFGS-B with finite-difference gradients); limited scaling.
• Synthetic, low-dimensional datasets.
• No hardware noise model; shot noise is ignored.