The time-index models are a class of time series forecasting models that map time-index features to forecasts in continuous space. Compared to the historical-value models, the time-index models can avoid the effect of data sampling frequency and are usually more expressive. However, the vanilla deep time-index model is weak in modeling the high-frequency components of time series and often requires the introduction of many parameters to enhance the modeling capability. Moreover, the time-index model learns only a mapping relationship and ignores the sequence relationship between temporal features, leading to a weak extrapolation capability in the forecast horizon. In this paper, inspired by the ability of quantum implicit neural representations to model the high-frequency components of signals with fewer parameters, we propose Quantum Time-Index Models with Reservoir (QuantumTime). Specifically, we introduce variational quantum circuits to address the challenge of representing high-frequency components in time series. Then, we introduce a reservoir that empowers QuantumTime with powerful extrapolation capabilities by exploiting the rich dynamical properties of reservoir computing. Ultimately, experiments conducted on chaotic datasets and various real-world datasets demonstrate that QuantumTime achieves highly competitive results compared to the state-of-the-art deep time-index model while reducing training parameters by at least 95%. Our approach provides a paradigm for utilizing potential quantum advantage in practical tasks.The time-index models are a class of time series forecasting models that map time-index features to forecasts in continuous space. Compared to the historical-value models, the time-index models can avoid the effect of data sampling frequency and are usually more expressive. However, the vanilla deep time-index model is weak in modeling the high-frequency components of time series and often requires the introduction of many parameters to enhance the modeling capability. Moreover, the time-index model learns only a mapping relationship and ignores the sequence relationship between temporal features, leading to a weak extrapolation capability in the forecast horizon. In this paper, inspired by the ability of quantum implicit neural representations to model the high-frequency components of signals with fewer parameters, we propose Quantum Time-Index Models with Reservoir (QuantumTime). Specifically, we introduce variational quantum circuits to address the challenge of representing high-frequency components in time series. Then, we introduce a reservoir that empowers QuantumTime with powerful extrapolation capabilities by exploiting the rich dynamical properties of reservoir computing. Ultimately, experiments conducted on chaotic datasets and various real-world datasets demonstrate that QuantumTime achieves highly competitive results compared to the state-of-the-art deep time-index model while reducing training parameters by at least 95%. Our approach provides a paradigm for utilizing potential quantum advantage in practical tasks.

ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD)Apr 4, 20251 citation

Time Evolution

Luigi E. Picasso

UNITEXT for physicsOct 26, 20150 citations

Time evolution

Theoretical and mathematical physicsSep 22, 20080 citations

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

J. M. Noriega, Luis Pesquera, M. A. Rodrguez +2 more

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times \ensuremath{\tau} larger than the deterministic relaxation time ${\mathit{t}}_{\mathit{d}}$ , we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times \ensuremath{\tau} larger than the deterministic relaxation time ${\mathit{t}}_{\mathit{d}}$, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Physical Review AAug 1, 199120 citations

Beyond Integrability Preserving Renormalization-Group Protocol in Non-Hermitian Hamiltonians with Time-Dependent Interaction Strengths

Parameshwar R. Pasnoori

It is well established that in time-dependent quantum systems, integrability preserving time-dependent interaction strengths are identical to the renormalization group (RG) trajectories of the corresponding static model when time ` $t$ ' in the driven model is identified with the logarithm of the cutoff ` $\logΛ$ ' of the static model. We refer to this integrability preserving driving as the RG protocol. In this work we extend the class of time-dependent integrable models to include non-Hermitian quantum models with time-dependent interaction strengths. Using the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that the constraints imposed by integrability are more general: The interaction strengths of the static model that flow in the RG follow the respective RG trajectories in the corresponding time-dependent model as described above. In addition, the interaction strengths of the static model that are RG invariant can either be constant or have a specific time-dependence in the corresponding time-dependent model which is constrained by integrability. Thus we establish that in the context of time-dependent non-Hermitian systems, the set of integrability preserving time-dependent strengths is larger than the set corresponding to the RG protocol.It is well established that in time-dependent quantum systems, integrability preserving time-dependent interaction strengths are identical to the renormalization group (RG) trajectories of the corresponding static model when time `$t$' in the driven model is identified with the logarithm of the cutoff `$\logΛ$' of the static model. We refer to this integrability preserving driving as the RG protocol. In this work we extend the class of time-dependent integrable models to include non-Hermitian quantum models with time-dependent interaction strengths. Using the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that the constraints imposed by integrability are more general: The interaction strengths of the static model that flow in the RG follow the respective RG trajectories in the corresponding time-dependent model as described above. In addition, the interaction strengths of the static model that are RG invariant can either be constant or have a specific time-dependence in the corresponding time-dependent model which is constrained by integrability. Thus we establish that in the context of time-dependent non-Hermitian systems, the set of integrability preserving time-dependent strengths is larger than the set corresponding to the RG protocol.

quant-pharXiv:2608.19519Aug 21, 20260 citations

Time Evolution

Emilio d’Emilio, Luigi E. Picasso

UNITEXT for physicsJan 1, 20170 citations

{\mathit{t}}_{\mathit{d}}

, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

t

' in the driven model is identified with the logarithm of the cutoff `

\logΛ

' of the static model. We refer to this integrability preserving driving as the RG protocol. In this work we extend the class of time-dependent integrable models to include non-Hermitian quantum models with time-dependent interaction strengths. Using the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that the constraints imposed by integrability are more general: The interaction strengths of the static model that flow in the RG follow the respective RG trajectories in the corresponding time-dependent model as described above. In addition, the interaction strengths of the static model that are RG invariant can either be constant or have a specific time-dependence in the corresponding time-dependent model which is constrained by integrability. Thus we establish that in the context of time-dependent non-Hermitian systems, the set of integrability preserving time-dependent strengths is larger than the set corresponding to the RG protocol.