Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function

TL;DR

This paper proposes a quantum-inspired sequence modeling framework where complex wave functions evolve unitarily, leveraging quantum interference and the Born rule to improve representational capacity over classical models.

Contribution

It introduces a novel quantum dynamics-based sequence model with a separation theorem showing its quadratic representational advantage over traditional real-valued models.

Findings

The model preserves state norm exactly at each step.

It solves certain disambiguation tasks with lower-dimensional states.

The framework provides a diagnostic for information flow via conserved currents.

Abstract

We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that rely on gating mechanisms to suppress competing hypotheses, our framework utilizes quantum interference: the Hamiltonian steers the phases of complex amplitudes so that conflicting interpretations cancel while compatible ones reinforce. The dynamics are strictly unitary, ensuring that the state norm is preserved exactly at every time step via a Cayley (Crank--Nicolson) discretization. Token probabilities are extracted using the Born rule, a quadratic measurement operator that couples magnitudes and relative phases. Our primary theoretical contribution is a separation theorem characterizing the representational advantage of this readout: we define a family of disambiguation tasks that a complex unitary model of dimension $N$ solves exactly, but which requires a state dimension of $\Omega(N^2)$ for any real-valued orthogonal model equipped with a standard affine-softmax readout. This quadratic gap arises because the Born rule implicitly lifts the $N$-dimensional state into the space of rank-one Hermitian matrices, accessing pairwise phase correlations that are inaccessible to linear projections. Finally, we derive a continuity equation for the latent probability mass, yielding conserved pairwise currents that serve as a built-in diagnostic for tracing information flow between dimensions.