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.
Related
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BibTeX
@misc{zhang2026generative,
title = {{Generative learning of time series with holographic quantum circuit sampling}},
author = {Bingzhi Zhang and Matthew W. Lee and Tom Finke and Quntao Zhuang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15083},
eprint = {2610.15083},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15083},
}
RIS
TY - UNPB
TI - Generative learning of time series with holographic quantum circuit sampling
AU - Bingzhi Zhang
AU - Matthew W. Lee
AU - Tom Finke
AU - Quntao Zhuang
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15083
UR - https://arxiv.org/abs/2610.15083
AB - 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.
ER -