Generative learning of time series with holographic quantum circuit sampling

Abstract:Quantum generative models face growing qubit requirements and concentrated loss landscapes when learning long time series. Here we introduce holographic quantum circuit sampling (HQCS), which combines mid-circuit measurements, qubit reuse and independently parameterized temporal blocks to generate trajectories with a fixed number of qubits. For Haar-random HQCS and a normalized exponential kernel, we prove inverse-polynomial bounds on maximum mean discrepancy loss variance, contrasting with exponential concentration in global Haar-random generators. For generic members of a family of nonstationary Markov processes, temporal parameterization reduces exact-generation gate counts from quadratic to linear in sequence length relative to a specified class of repeated shared-block generators. Simulations demonstrate learning of Gaussian autoregressive processes and historical Volatility Index (VIX) trajectories, with the latter achieving over tenfold lower maximum mean discrepancy than the tested classical benchmarks. These results establish a framework for quantum time-series generation with fixed qubit requirements and provable avoidance of exponential loss concentration as sequence length grows.

arXiv:2610.15083 [quant-ph]

(or arXiv:2610.15083v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.15083 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.