Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1911.02767 · Physical Review A

Robust inference of memory structure for efficient quantum modeling of stochastic processes

Matthew Ho, Mile Gu, Thomas J. Elliott

Published Mar 19, 2020• 13 citations
arXivHTMLPDF

Abstract

A growing body of work has established the modeling of stochastic processes as a promising area of application for quantum technologies; it has been shown that quantum models are able to replicate the future statistics of a stochastic process while retaining less information about the past than any classical model must, even for a purely classical process. Such memory-efficient models open a potential future route to study complex systems in greater detail than ever before and suggest profound consequences for our notions of structure in their dynamics. Yet, to date methods for constructing these quantum models are based on having a prior knowledge of the optimal classical model. Here, we introduce a protocol for blind inference of the memory structure of quantum models---tailored to take advantage of quantum features---direct from time-series data, in the process highlighting the robustness of their structure to noise. This in turn provides a way to construct memory-efficient quantum models of stochastic processes while circumventing certain drawbacks that manifest solely as a result of classical information processing in classical inference protocols.

DOI
10.1103/physreva.101.032327

Related papers

Memory-efficient tracking of complex temporal and symbolic dynamics with quantum simulators

Thomas J. Elliott, Andrew J. P. Garner, Mile Gu

Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of the system than the optimal classical models. We extend these results to general temporal and symbolic dynamics. Our systematic protocol for quantum model construction relies only on an elementary description of the dynamics of the process. This circumvents restrictions on corresponding classical construction protocols, and allows for a broader range of processes to be modelled efficiently. We illustrate our method with an example exhibiting an apparent unbounded memory advantage of the quantum model compared to its optimal classical counterpart.

arXiv:1803.05426•New Journal of Physics•Dec 12, 2018•18 citations

Optimal stochastic modeling with unitary quantum dynamics

Qing Liu, Thomas J. Elliott, Felix C. Binder +2 more

Isolating past information relevant for future prediction is central to quantitative science. Quantum models offer a promising approach, enabling statistically faithful modeling while using less past information than any classical counterpart. Here we introduce a class of phase-enhanced quantum models, representing the most general means of simulating a stochastic process unitarily in causal order. The resulting constructions surpass previous state-of-art methods---both in reducing the information they need to store about the past and in the minimal memory dimension they require to store this information. Moreover, these two features are generally competing factors in optimization---leading to an ambiguity in optimal modeling that is unique to the quantum regime. Our results simultaneously offer quantum advantages for stochastic simulation and illustrate further qualitative differences between classical and quantum notions of complexity.

arXiv:1810.09668•Physical Review A•Jun 18, 2019•39 citations

Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes

Thomas J. Elliott, Mile Gu

Abstract Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.

arXiv:1704.04231•npj Quantum Information•Feb 16, 2018•37 citations

Dimension reduction in quantum sampling of stochastic processes

Chengran Yang, M. Florido-Llinas, Mile Gu +1 more

Abstract Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the stochastic process, which requires a memory system to propagate correlations between the past and future of the process. Here, we introduce a method of lossy quantum dimension reduction that allows this memory to be compressed, not just beyond classical limits, but also beyond current state-of-the-art quantum stochastic sampling approaches. We investigate the trade-off between the saving in memory resources from this compression, and the distortion it introduces. We show that our approach can be highly effective in low distortion compression of both Markovian and strongly non-Markovian processes alike. We further discuss the application of our results to quantum stochastic modelling more broadly.

arXiv:2404.10338•npj Quantum Information•Feb 28, 2025•4 citations

Embedding memory-efficient stochastic simulators as quantum trajectories

Thomas J. Elliott, Mile Gu

By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a host of computational advantages. One such advantage lies in the field of stochastic modeling, where it has been shown that quantum stochastic simulators can operate with a lower memory overhead than their best classical counterparts. This advantage is particularly pronounced for continuous-time stochastic processes; however, the corresponding quantum stochastic simulators heretofore prescribed operate only on a quasi-continuous-time basis and suffer an ever-increasing circuit complexity with increasing temporal resolution. Here, by establishing a correspondence with quantum trajectories (a method for modeling open quantum systems), we show how truly continuous-time quantum stochastic simulators can be embedded in such open quantum systems, bridging this gap and obviating previous constraints. We further show how such an embedding can be made for discrete-time stochastic processes, which manifest as jump-only trajectories, and discuss how viewing the correspondence in the reverse direction provides a means of studying structural complexity in quantum systems themselves. Published by the American Physical Society 2024

arXiv:2402.04708•Physical Review A•Feb 26, 2024•4 citations

Quantum Coarse Graining for Extreme Dimension Reduction in Modeling Stochastic Temporal Dynamics

Thomas J. Elliott

Stochastic modeling of complex systems plays an essential, yet often computationally intensive, role across the quantitative sciences.Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks.Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while-arguably more practical-reductions in memory dimension are not always possible.Here, we address the case of lossy compression for quantum stochastic modeling of continuous-time processes, introducing a method for coarse graining in quantum state space that drastically reduces the requisite memory dimension for modeling temporal dynamics while retaining near-exact statistics.In contrast to classical coarse graining, this compression is not based on sacrificing temporal resolution and brings memory-efficient high-fidelity stochastic modeling within reach of present quantum technologies.

arXiv:2105.06831•PRX Quantum•Jun 16, 2021•12 citations
A growing body of work has established the modeling of stochastic processes as a promising area of application for quantum technologies; it has been shown that quantum models are able to replicate the future statistics of a stochastic process while retaining less information about the past than any classical model must, even for a purely classical process. Such memory-efficient models open a potential future route to study complex systems in greater detail than ever before and suggest profound consequences for our notions of structure in their dynamics. Yet, to date methods for constructing these quantum models are based on having a prior knowledge of the optimal classical model. Here, we introduce a protocol for blind inference of the memory structure of quantum models---tailored to take advantage of quantum features---direct from time-series data, in the process highlighting the robustness of their structure to noise. This in turn provides a way to construct memory-efficient quantum models of stochastic processes while circumventing certain drawbacks that manifest solely as a result of classical information processing in classical inference protocols.
Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of the system than the optimal classical models. We extend these results to general temporal and symbolic dynamics. Our systematic protocol for quantum model construction relies only on an elementary description of the dynamics of the process. This circumvents restrictions on corresponding classical construction protocols, and allows for a broader range of processes to be modelled efficiently. We illustrate our method with an example exhibiting an apparent unbounded memory advantage of the quantum model compared to its optimal classical counterpart.
Isolating past information relevant for future prediction is central to quantitative science. Quantum models offer a promising approach, enabling statistically faithful modeling while using less past information than any classical counterpart. Here we introduce a class of phase-enhanced quantum models, representing the most general means of simulating a stochastic process unitarily in causal order. The resulting constructions surpass previous state-of-art methods---both in reducing the information they need to store about the past and in the minimal memory dimension they require to store this information. Moreover, these two features are generally competing factors in optimization---leading to an ambiguity in optimal modeling that is unique to the quantum regime. Our results simultaneously offer quantum advantages for stochastic simulation and illustrate further qualitative differences between classical and quantum notions of complexity.
Abstract Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.
Abstract Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the stochastic process, which requires a memory system to propagate correlations between the past and future of the process. Here, we introduce a method of lossy quantum dimension reduction that allows this memory to be compressed, not just beyond classical limits, but also beyond current state-of-the-art quantum stochastic sampling approaches. We investigate the trade-off between the saving in memory resources from this compression, and the distortion it introduces. We show that our approach can be highly effective in low distortion compression of both Markovian and strongly non-Markovian processes alike. We further discuss the application of our results to quantum stochastic modelling more broadly.
By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a host of computational advantages. One such advantage lies in the field of stochastic modeling, where it has been shown that quantum stochastic simulators can operate with a lower memory overhead than their best classical counterparts. This advantage is particularly pronounced for continuous-time stochastic processes; however, the corresponding quantum stochastic simulators heretofore prescribed operate only on a quasi-continuous-time basis and suffer an ever-increasing circuit complexity with increasing temporal resolution. Here, by establishing a correspondence with quantum trajectories (a method for modeling open quantum systems), we show how truly continuous-time quantum stochastic simulators can be embedded in such open quantum systems, bridging this gap and obviating previous constraints. We further show how such an embedding can be made for discrete-time stochastic processes, which manifest as jump-only trajectories, and discuss how viewing the correspondence in the reverse direction provides a means of studying structural complexity in quantum systems themselves. Published by the American Physical Society 2024
Stochastic modeling of complex systems plays an essential, yet often computationally intensive, role across the quantitative sciences.Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks.Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while-arguably more practical-reductions in memory dimension are not always possible.Here, we address the case of lossy compression for quantum stochastic modeling of continuous-time processes, introducing a method for coarse graining in quantum state space that drastically reduces the requisite memory dimension for modeling temporal dynamics while retaining near-exact statistics.In contrast to classical coarse graining, this compression is not based on sacrificing temporal resolution and brings memory-efficient high-fidelity stochastic modeling within reach of present quantum technologies.