Practical Quantum Reservoir Computing in Rydberg Atom Arrays

TL;DR

This paper assesses how two quantum reservoir computing architectures—single-step-QRC (SS-QRC) and multi-step-QRC (MS-QRC)—perform on a Rydberg-atom array under realistic constraints including dynamical phases, decoherence, and finite-shot sampling. It uses randomized and derandomized classical shadows to manage readout overhead and analyzes both non-temporal and time-series tasks via information processing capacity (IPC). The key finding is that MS-QRC shows strong nonlinear processing near phase transitions but its advantages collapse under sampling noise due to poor convergence, while SS-QRC remains robust across conditions, making it a practical choice for NISQ-era quantum ML. The work provides guidance for architecture selection in quantum ML on neutral-atom platforms and demonstrates the importance of measurement strategies in realizing practical QRC performance.

Abstract

Quantum reservoir computing (QRC) is a promising quantum machine learning framework for near-term quantum platforms, yet the performance of different QRC architectures under realistic constraints remains largely unexplored. Here, we provide a comparative numerical study of single-step-QRC (SS-QRC) and multi-step-QRC (MS-QRC) architectures implemented on a Rydberg atom array. We demonstrate that while MS-QRC performance is highly sensitive to the underlying dynamical phase of matter and decoherence, SS-QRC exhibits greater robustness. Using the randomized measurement toolbox to mitigate measurement overhead, we reveal that sampling noise undermines the convergence property required for MS-QRC. This leads to a significant reduction in the information processing capacity (IPC) of MS-QRC, deteriorating its performance on nonlinear time-series benchmarks. In contrast, SS-QRC maintains high IPC and accuracy across both temporal and non-temporal tasks. Our results suggest SS-QRC as a preferred candidate for near-term practical applications due to its resilience to system configurations and statistical noise.

Figures (5)

• Figure 1: Schematic of quantum reservoir computing (QRC) with neutral atom arrays. (a) The reservoir consists of neutral atoms trapped in optical tweezers. Global Rydberg excitation drives atom-atom interactions, nonlinearly mapping inputs encoded in local detunings $\Delta_i(t)$ into an exponentially large Hilbert space. Outputs are extracted by measuring single- and two-site Pauli operators. (b) The single-step-QRC (SS-QRC) architecture. For each input $\boldsymbol{x}^{(m)}$, the reservoir evolves via a single CPTP map $\mathcal{E}(\boldsymbol{x}^{(m)})$. The measured signals $\boldsymbol{v}^{(m)}$ are processed by a linear layer with weights $\boldsymbol{w}$ trained via ridge regression. (c) The multi-step-QRC (MS-QRC) architecture. The reservoir processes a time-series sequence $\boldsymbol{x}^{(1)},\dots,\boldsymbol{x}^{(m)}$ through sequential evolution to capture temporal dependencies, followed by measurement and linear post-processing.
• Figure 2: System configuration of an array of 10 atoms. (a) The triangular lattice of 10 atoms, where the positions of each atom (green stars) are normally distributed from the ideal lattice sites (empty circles). (b) The phase diagram of the atom array shown in (a), averaged over 1000 realizations of the atoms' positions at $\eta=0$. The parameters $(\Delta/\Omega=-0.5,\ a/R_b=1)$ marked by the black cross near the phase boundary are used for subsequent machine learning tasks. (c) Out-of-time-order correlator $F(\tau)$ as a function of duration $\tau$, with $\Delta/\Omega=-0.5$, $a/R_b=1$, $\eta=0$. (d) Convergence of MS-QRC characterized by the trace distance $D(\rho^{(m)},\rho'^{(m)})$, with the system starting from two different initial states $\rho^{(0)}$ and $\rho'^{(0)}$, and $\Delta/\Omega=-0.5$, $a/R_b=1$, $\gamma/\Omega=0.95$, $\tau=10/\Omega$, $\eta/\Omega=0.1$. The shaded area in (c-d) denotes the standard deviation across 10 realizations of the atoms' positions.
• Figure 3: Performance with respect to the global bias detuning $\Delta$ and the decay rate $\gamma$. (a-b) The total information processing capacity (IPC), denoted as $C_\mathrm{tot}$, of MS-QRC with respect to the global bias detuning $\Delta$ and decay rate $\gamma$. $C_\mathrm{tot}$ is decomposed according to the order of nonlinearity, represented by bars with different colors. (c-d) The total IPC of SS-QRC with respect to the global bias detuning $\Delta$ and decay rate $\gamma$. The dashed lines in (a) and (c) indicates the phase boundaries. The results are averaged over 5 realization of the atoms' positions, with $a/R_b=1$, $\gamma/\Omega=0.95$, $\eta/\Omega=0.1$. The IPC are calculated using 1000 input time series uniformly sampled from [-1, 1] where the first 200 time steps are used for washout.
• Figure 4: Performance of the SS-QRC on classification tasks, using the randomized measurement toolbox. (a) Classification accuracy on the Iris dataset, with $\Delta/\Omega=-0.5$, $a/R_b=1$, $\gamma/\Omega=0.95$, $\tau=10/\Omega$, $\eta/\Omega=0.1$. (b) Classification accuracy of SS-QRC on the entanglement-separability classification task, with $a/R_b=1$, $\gamma/\Omega=0.95$, $\tau=16/\Omega$. The dashed lines in (a-b) indicate the classification accuracy in the asymptotic limit ($N_s=\infty$). (c) Measurement error in the Iris dataset classification task, evaluated by the Frobenius norm $\|\boldsymbol{V}-\boldsymbol{V}_\mathrm{true}\|_\mathrm{Fro}$, where $\boldsymbol{V}_\mathrm{true}$ denotes the matrix of readout signals without sampling noise. (d) Measurement error in the entanglement-separability classification task. The error bars are standard deviations across 10 realizations of the measurement process.
• Figure 5: Performance of MS-QRC and SS-QRC on time-series prediction tasks under sampling noise using the derandomized classical shadow protocol. (a) The IPC of MS-QRC versus the number of measurement shots $N_s$. (b) Convergence of MS-QRC characterized by $\|\boldsymbol{v}^{(m)}-\boldsymbol{v}'^{(m)}\|_2$, with the reservoir starting from two different initial states. The dashed blue curve corresponds to the asymptotic limit. (c) The IPC of the SS-QRC. The results in (a) and (c) are averaged over 5 realizations of the atoms positions. (d) The normalized root mean square error (NRMSE) of MS-QRC and SS-QRC on the second-order NARMA task, with the dashed lines corresponding to $N_s=\infty$ for the two models. Error bars are standard deviations across 10 realizations of the derandomized classical shadow protocol. (e) The predictions of MS-QRC and SS-QRC on the second-order NARMA task at $N_s=2\times 10^5$. The parameters used in (a-e) are $\Delta/\Omega=-0.5$, $a/R_b=1$, $\gamma/\Omega=0.95$, $\eta/\Omega=0.1$.