This research introduces an innovative method of lossy quantum dimension reduction for efficiently sampling and analyzing stochastic processes across scientific disciplines. The approach addresses a fundamental challenge: the exponential growth in computational complexity when modeling stochastic processes over time.
The authors focus on compressing the memory system required to propagate correlations between past and future states in quantum sample states (q-samples). Traditional approaches, including Monte Carlo methods, require substantial memory resources to carry information about temporal correlations. While quantum information processing already offers advantages over classical methods—providing quadratic speedups and enhanced expressivity—this new technique pushes those benefits further.
The paper’s key innovation is a systematic lossy quantum dimension reduction approach that determines a new circuit with fixed memory dimension to approximate the original q-sample. This method draws inspiration from matrix product state truncation techniques and exploits a correspondence between matrix product states and q-samples.
The quantum sampling approach works through a recurrent circuit structure that propagates a memory system to interact with blank ancillae, sequentially building the q-sample state timestep by timestep. This circuit design scales linearly with the number of timesteps rather than exponentially. However, the memory system dimension can still grow large for complex processes with strong temporal correlations—which is where the proposed compression technique provides significant benefits.
Testing demonstrates that this approach yields high-fidelity approximations for both Markovian processes (with limited temporal dependencies) and highly non-Markovian processes (with strong temporal correlations). The authors explore the tradeoff between compression ratio and distortion, showing their method effectively balances memory savings against accuracy.
Notably, the technique achieves compression beyond both current state-of-the-art lossless quantum dimension reduction for quantum models and lossy compression for classical models, while maintaining highly accurate reconstruction of output statistics.
The research has broad applications across numerous fields including evolutionary biology, chemistry, geophysics, astrophysics, financial markets, traffic modeling, and natural language processing—all areas where complex stochastic processes play a crucial role. By mitigating the computational resource requirements for analyzing these processes, this work contributes valuable tools for scientific modeling and simulation that could enable deeper insights and more efficient analysis of complex systems.
Reference: Yang, C., Florido-Llinàs, M., Gu, M. et al. Dimension reduction in quantum sampling of stochastic processes. npj Quantum Inf 11, 34 (2025). doi:10.1038/s41534-025-00978-2
