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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Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout. This separation reduces reliance on repeated quantum parameter updates and avoids the barren plateaus associated with variational circuit training. Its computational power is often attributed to the exponentially large Hilbert space of the quantum system. However, the memory, nonlinearity, and expressivity that determine what a reservoir can actually compute depend jointly on the input encoding, quantum evolution, observables, measurement, and readout, not on Hilbert space dimension alone. On hardware, these capabilities are further constrained by finite sampling, hardware noise, measurement backaction, and the cost of estimating observables, so a large state space alone does not guarantee useful computation. In this survey, we develop a common system model that connects these components and use it to organize QRC foundations, computational properties, reservoir architectures, operating protocols, and physical implementations. We examine spin, photonic, superconducting, bosonic, neutral atom, and other analog platforms, together with applications, software and high performance computing support, benchmarking, and reproducibility. The analysis distinguishes hardware demonstrations from simulations and identifies the assumptions and resources that govern comparisons across implementations. Current results do not establish a broad quantum advantage over well matched classical reservoirs. We therefore specify the resource accounting, benchmark standards, and theoretical criteria needed to evaluate claims of quantum advantage.

Abstract

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