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

2026/02/24 by Ahmed Nebli, Hadi Saadatdoorabi, Kevin Yam · 1 voice
Computer Science · Materials Science · Physics and Astronomy · #Hamiltonian (control theory) #Hermitian matrix #Hilbert space #Machine Learning in Materials Science #Pairwise comparison #Phase space #Probability amplitude #Quadratic equation #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Quantum state #Sequence (biology) #cs.AI #cs.LG #quant-ph

paper · pdf · doi:10.48550/arxiv.2602.22255

openalex publication_date 2026/02/24 · arxiv published 2026/02/24 · arxiv updated 2026/02/24 · openalex created_date 2026/02/28 · openalex updated_date 2026/07/28

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 Ω(N²) 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.

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Discussions

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