Efficient time-series prediction on NISQ devices via time-delayed quantum extreme learning machine

TL;DR

Experiments demonstrate that TD-QELM consistently outperforms conventional quantum reservoir computing in prediction accuracy and noise robustness and highlight TD-QELM as a practical and scalable framework for time-series learning on current NISQ hardware.

Abstract

We proposed a time-delayed quantum extreme learning machine (TD-QELM) for efficient time-series prediction on noisy intermediate-scale quantum (NISQ) devices. By encoding multiple past inputs simultaneously, TD-QELM achieves shallow circuit depth independent of sequence length, thereby, mitigating noise accumulation and reducing computational complexity. Experiments using the NARMA benchmark on both noiseless simulations and IBM's 127-qubit processor demonstrate that TD-QELM consistently outperforms conventional quantum reservoir computing in prediction accuracy and noise robustness. These results highlight TD-QELM as a practical and scalable framework for time-series learning on current NISQ hardware.

Figures (4)

• Figure 1: Conceptual Diagrams of QRC and TD-QELM. (a) In the restarting protocol, input encoding and unitary evolution $U_R$ are sequentially applied at each timestep to incorporate past information. This causes circuit depth and computational cost to grow quadratically with sequence length $M$. (b) The current input $s_t$ and $N-1$ time-delayed inputs ${s_{t}, s_{t-1}, \dots, s_{t-(N-1)}}$ are simultaneously encoded into $N$ qubits, keeping the circuit shallow regardless of $M$.
• Figure 2: (a) Connectivity map of the qubits used in the experiment within the ibm_kawasaki device topology (partially shown), where each $q_i$ represents a qubit. The connections define a hardware-specific topology $E$. (b) Hardware-efficient circuit using Trotterization, designed to implement a multi-qubit quantum system under real-device connectivity constraints. This design reduces gate operations while maintaining sufficient entanglement on NISQ hardware.
• Figure 3: Average NMSE of TD-QELM and QRC as a function of input length $M$ under ideal noiseless simulation ($\gamma = 0$), a hardware-mimicking noise model (FakeKawasaki, denoted as "Fake" in the legend), and a real NISQ device (ibm_kawasaki, denoted as "ibm"), using 10% washout, 70% training, and 20% testing. $N_S = 6$ sites are considered with $N_V = 1$ multiplexing. TD-QELM maintains low NMSE even for long input sequences, whereas QRC shows rapid performance degradation. Error bars indicate the range between the maximum and minimum values over 10 trials.
• Figure 4: Time-series output for the NARMA10 task obtained on the ibm_kawasaki quantum hardware. The black curve shows the target signal (NARMA10), while the orange and green curves correspond to the outputs of TD-QELM (ibm) and QRC (ibm), respectively.