Good questions make
better experiments.

In progress Quantum machine learning

Can a parameterized quantum circuit learn context-dependent next-token distributions with better parameter efficiency or computational scaling than a comparably sized classical model?

How the lab’s work fits together: our Rust state-vector simulator runs the circuits, aaronnet runs the classical baselines, and the transformer work is the classical comparator we measure against.

Planned approach.

• Small synthetic next-token tasks with controlled context dependence and a small vocabulary.
• Compare circuits against classical models with matched parameter counts: an MLP, a small transformer, and a matrix product state (MPS) Born machine.
• Measure parameter efficiency on the simulator as held-out cross-entropy against parameter count.
• Treat computational scaling separately. Argue it in gate count, circuit depth, and measurement shots, never in simulator wall time, since state-vector simulation costs 2ⁿ by construction.
• Count shots in any cost comparison, because hardware estimates probabilities by sampling while the simulator reads them exactly.

Related work.

• Anschuetz, Hu, Huang, and Gao 2023, “Interpretable Quantum Advantage in Neural Sequence Learning” (PRX Quantum).
• Anschuetz and Gao 2024, “Arbitrary Polynomial Separations in Trainable Quantum Machine Learning” (arXiv:2402.08606).
• McClean et al. 2018, “Barren plateaus in quantum neural network training landscapes.”

Their sequence models are continuous-variable, built from Gaussian operations, while we study qubit circuits; we expect trainability at scale to be the main obstacle.

In progress Neural architectures

What, exactly, does the architecture make possible?

We start with small transformers we can build and inspect. By changing one component at a time (attention, residual pathways, normalization, or positional information), we can ask which behaviors depend on which design choices.

• How do learned representations change across depth and training?
• Which capabilities survive an architectural ablation?
• What happens as context length and compute budgets change?

Transformer build log →

Plan Model behavior

When is a correct answer evidence of understanding?

Benchmarks measure performance, but not necessarily how a model arrived at it. Small, carefully designed tasks can help distinguish durable problem-solving strategies from shortcuts.

• When does a network learn a rule rather than memorize a pattern?
• What happens when task length or distribution changes?
• Can internal measurements explain specific failures?

Follow in the notebook →

In progress Classical and quantum systems

What changes when the model of computation changes?

Quantum computing is worth understanding on its own terms. Our entry point is the underlying mathematics: complex amplitudes, operators, interference, and the algorithms that use them. This line of work also provides the substrate for our central question: the simulator is what we use to train and evaluate the quantum circuits in that comparison.

• How does state-vector simulation expose unitary evolution?
• How do implementation costs scale with qubit count?
• Where do classical and quantum abstractions diverge?

Read the simulator note →