From quantum feature maps to quantum reservoir computing: perspectives and applications

TL;DR

The paper investigates quantum reservoir computing (QRC) as a hybrid framework blending quantum evolutions in high-dimensional Hilbert spaces with classical processing. It develops a neutral-atom–based hQCRC workflow that uses quantum feature maps to embed inputs and a classical readout to train the reservoir, demonstrated on chaotic time-series forecasting with Lorenz63. The authors discuss critical challenges including fading memory, readout overhead, and non-Markovian effects, and argue that QRC provides a natural path to scale reservoir computing on near-term quantum hardware. The work offers a modular, hardware-adaptive blueprint for integrating quantum reservoirs into RC tasks and outlines directions for benchmarking and automated architecture search.

Abstract

We explore the interplay between two emerging paradigms: reservoir computing and quantum computing. We observe how quantum systems featuring beyond-classical correlations and vast computational spaces can serve as non-trivial, experimentally viable reservoirs for typical tasks in machine learning. With a focus on neutral atom quantum processing units, we describe and exemplify a novel quantum reservoir computing (QRC) workflow. We conclude exploratively discussing the main challenges ahead, whilst arguing how QRC can offer a natural candidate to push forward reservoir computing applications.

Figures (3)

• Figure 1: Impact of various feature map encodings. (Left) Single-qubit case with 1D data $u$ on the outcome, expressed as the expectation value of a state $R_Z[f(u)]\ket+$. (Middle) 2-qubit case, where two types of observables are extracted, as distinguished by dashed versus solid lines. The colours identify different feature map encodings (identity and $\tanh$). (Right) 8-qubit case encoding a 3D time-series, i.e. $\dim(u)=3$, and values of various colour-encoded observables as a function of time.
• Figure 2: A representation of the 3 phases of the suggested hybrid Quantum Reservoir Computing protocol. A data encoding manipulates the initial vector $u_t$ into a modified $Y_i(t)$ which is then encoded into the quantum circuit, where $i$ indicates the layer in which the data is injected. The encoding is here exemplified for a Neutral Atom architecture compatible with Eq. \ref{['eq:NA']}, and processes the input $Y_i^{(j)}(t)$ according to the chosen (sets of) free parameters $j$ such as $\Omega, \delta, \phi$, alternatively operating at a global or local level (details in the main text). The pulse sequences shown for the circuit encoding are generated in Pulsersilverio2022pulser. The readout from the quantum circuit $M_t$ is finally post-processed in a reservoir-like fashion compatible with the relation \ref{['eq:reservoir_state']}, and trained until $r_t$ reproduces the target dataset. Phases implemented in classical (quantum) devices are encircled in dark (light) gray boxes.
• Figure 3: Prediction phase of the normalized Lorenz63 time-series benchmark (black) for $x, y$ and $z$ components (left to right). The red line represents a numerical simulation of the hQCRC framework in \ref{['Eq:ESN']} (i.e. $f_M\equiv id$), whereas the blue line synthetically retrieves a classical-phase only performance by imposing $f_M\equiv0$ in the same equation, while the green line uses $f_X\equiv 0$, i.e. the reservoir $r_t$ depends only on measurements extracted from the quantum states $M_t$. Finally, the teal line depicts the best performing setup for classical RC. Implementations details of the circuit in the main text. The shaded region describes $\pm$ standard deviation over 20 random seeds of quantum reservoirs.