Digital Twin Modeling of Quantum Dynamical Systems: Dissipative Quantum Reservoir Computing

Abhijit Sen; Bikram Keshari Parida; Shital Chauhan; Mahima Arya; Denys I. Bondar

quant-phSep 29, 2026

Digital Twin Modeling of Quantum Dynamical Systems: Dissipative Quantum Reservoir Computing

Authors: Abhijit Sen, Bikram Keshari Parida, Shital Chauhan, Mahima Arya, Denys I. Bondar

Organizations: Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA · Department of Data Science, Dongduk Women’s University, Seoul, South Korea · SSJDWSSSS Government Post Graduate College, Ranikhet 263645, India

Abstract

Modeling the response of driven many-body quantum systems from input--output data is difficult: the dynamics are nonlinear, history dependent, and expensive to simulate as system size grows. A paradigmatic case is High-Harmonic Generation~(HHG), where a strong field drives a medium to emit radiation that is highly sensitive to the drive and encodes long-range temporal correlations. We introduce a dissipative quantum reservoir computing~(DQRC) framework that builds a digital twin of such a system, learning its input--output map directly from data while the reservoir---itself a small open quantum system---stays fixed and only a classical readout is trained. We show that a minimal single-qubit reservoir reproduces the HHG response of a substantially larger Ising spin chain, and on a representative benchmark matches and on several metrics surpasses previously reported temporal convolutional and Kolmogorov--Arnold-network models, while using a simpler, physically realizable system. A single fixed reservoir further generalizes across a broad range of drives, indicating that it learns a shared physical response structure rather than memorizing trajectories. These results establish dissipative quantum reservoirs as compact, physically grounded digital twins for nonlinear, memory-dependent quantum dynamics. Code is available at https://github.com/AI-and-Quantum-Computing/DQuRC.

Figures & tables

Figure 1: Optics as an input–output problem. An input field $\mathbf{E}(t)$ (red) interacts with a medium (beaker) to produce an output field $\mathbf{Y}(t)$ (green). A quantum Reservoir with trainable readout, the readout layer trained on $(\mathbf{E}(t),\mathbf{Y}(t))$ pairs, serves as a surrogate model of the medium, enabling prediction of $\mathbf{Y}(t)$ for previously unseen inputs $\mathbf{E}(t)$ .

Figure 2: Schematic overview of Classical Reservoir Computing (CRC), illustrating the separation between a fixed nonlinear dynamical system (the reservoir) and a trainable linear readout. The input signal $u(t)$ is discretized and injected via the input weight matrix $W_{\mathrm{in}}$ . The reservoir state $x(k)$ evolves according to $x(k)=f\!\left(W\,x(k-1)+W_{\mathrm{in}}\,u(k)\right)$ , and the output $y(k)$ is obtained through a trained linear readout $y(k)=W_{\mathrm{out}}\,x(k)$ , where only $W_{\mathrm{out}}$ is optimized during training.

Figure 3: Schematic illustration of the transition from classical reservoir computing (CRC) to quantum reservoir computing (QRC). (Left) A classical dynamical system with a fixed reservoir and trained readout layer. (Center) Replacement of the classical reservoir with an $N$ -qubit quantum system. (Right) Full QRC architecture: input is encoded at each time step into the first qubit, the reservoir evolves unitarily in the $2^{N}$ -dimensional Hilbert space, and observables are extracted via a classical readout layer to produce the output vector.

Figure 4: Dataset construction and feeding strategy for input–output time-series learning with quantum reservoir computing. Continuous-time input stimuli $h(t)$ and output responses $Y(t)$ are first sampled on a uniform grid with time step $\Delta t$ , producing fixed-length vectors of length $T=512$ . Each row of the dataset corresponds to one complete system run, represented as a paired sequence $\mathbf{h}^{(i)}\rightarrow\mathbf{Y}^{(i)}$ . The full dataset $\mathscr{D}(F_{0})$ is split into training and test subsets. During learning, each input sequence is fed sequentially into the quantum reservoir, whose measured observables generate temporal reservoir features. A trainable readout then maps these features to the predicted output sequence.

Method	Architecture	$N_{\omega}$	$R^{2}>0.90$ (%)	$R^{2}>0.95$ (%)
QRC	$N=1$ qubit	200	90	75
QRC	$N=1$ qubit	400	97.5	93.75
KAN	[500,100,500]	200	82.5	75.0
KAN	[500,400,400,500]	600	95.8	95.8

Table 1: Reconstruction performance in the weak-drive regime (

F_{0}=10

) for QRC with

N=1

reservoir [Eq. ( 13 )], compared against KAN-based results from Ref. [ 34 ] at equivalent amplitude (

A=10

). Results report the percentage of test cases exceeding threshold values of

R^{2}>0.90

and

R^{2}>0.95

$N_{\omega}$	$N$	$R^{2}$	$R^{2}>0.90$ (%)	$R^{2}>0.95$ (%)
1000	1	0.9984	94.5	92.0
	2	0.9999	100	100
1500	1	0.9984	94.0	92.6
2000	1	0.9989	95.0	94.0
3700	1	0.9997	99.59	98.38

Table 2: Performance of the DQRC readout as a function of the number of training data points

N_{\omega}

, for

N=1

and

N=2

reservoir qubits [ Eq. ( 13 )]. The

N=2

case saturates at

100\%

from

N_{\omega}=1000

onward (entries omitted);

N=1

reaches

R^{2}>0.90

99.59\%

and

R^{2}>0.95

98.38\%

of cases by

N_{\omega}=3700

, indicating that adding a qubit accelerates convergence.

$N_{\mathrm{total}}$	$R^{2}_{\mathrm{th}}$	Passed / Total	Pass rate (%)
$4000$	$0.90$	$710/800$	$88.75$
$4000$	$0.95$	$687/800$	$85.88$

Table 3: Performance of the multi-amplitude QRC readout on the held-out test set (

N_{\mathrm{test}}=800

samples,

N_{\mathrm{total}}=4000

F_{0}\in[1,20]

), using a single QRC +PCA(

d=15

)+KRR model. Pass rates are reported at two

R^{2}

thresholds.

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