Configured Quantum Reservoir Computing for Multi-Task Machine Learning

Quantum computing is rapidly advancing, with NISQ devices showing promise for practical applications. Quantum reservoir computing (QRC) is a machine learning framework that leverages the complex quantum superposition states created by the reservoir's dynamics to perform machine learning tasks. Current QRC models use a fixed Hamiltonian, limiting their performance. This paper introduces a novel approach that uses a genetic algorithm to configure the Hamiltonian parameters, optimizing the reservoir dynamics for enhanced learning. This approach is tested on complex tasks not typically handled by QRC, aiming to demonstrate the potential of QRC for tackling real-world problems and contribute to artificial general intelligence.

The past two decades have seen significant advancements in quantum technologies, with demonstrations of quantum advantage in tasks like random circuit sampling and boson sampling. Various quantum computing approaches, including the quantum approximate optimization algorithm (QAOA), variational quantum eigensolver (VQE), and adiabatic quantum computation, have been developed. QRC has emerged as a promising framework for machine learning, harnessing the power of quantum computation through the mapping of input signals to a high-dimensional quantum space. However, existing QRC models utilize fixed Hamiltonians, and their learning capabilities are limited to simple tasks like parity checking and short-term memory. Previous work has suggested engineering reservoir dynamics near the phase boundary of quantum ergodicity or leveraging quantum criticality to enhance QRC performance. This research builds upon these findings, introducing a novel method to overcome the limitations of fixed Hamiltonians.

The proposed configured QRC uses a parameterized Hamiltonian H(θ), where θ represents controllable parameters optimized by a genetic algorithm. The input and output are time sequences. Input signals are sequentially injected into the quantum reservoir, which involves projective measurements of reservoir qubits followed by resetting them to states encoding the input signal. The reservoir evolves for a specific duration (τ) between injections. Pauli measurements are performed, and the results (Aθ) are transformed to compute outputs using a linear regression model (yₖ = W ⋅ Aθ + B). The weights (W and B) are determined by minimizing the difference between the output and the target. The genetic algorithm optimizes the quantum reservoir parameters (θ) by minimizing the objective function, which is the sum of squared errors across various input sequences. A fully connected transverse-field Ising model is used as the quantum reservoir, with parameters Jᵢⱼ and hᵢ. Multi-task learning is achieved using a single quantum reservoir with task-dependent weights for the linear regression model. The normalized mean squared error (NMSE) is used to evaluate the learning performance across different tasks. A comparison with echo state networks (ESNs), a classical reservoir computing method, is conducted to highlight the quantum advantage. The effect of quantum coherence is investigated using synthetic models with controllable coherence levels, employing measurements in different bases for input encoding and systematically varying the level of quantum entanglement in the reservoir.

The configured quantum reservoir computing demonstrated superior performance across diverse tasks: 1. **Gene Regulatory Networks:** The approach accurately predicted the dynamics of a synthetic oscillatory network of transcriptional regulators and a chaotic motif in gene regulatory networks, capturing oscillations and chaotic behavior with high precision (NMSE at the level of 10⁻¹⁰ and 10⁻⁴ respectively). The quantum reservoir correctly modeled the mutual inhibition and oscillatory behavior of the transcriptional regulator network and the chaotic features of the motif, even with different parameters used for training and testing datasets. The discrepancy observed in predicting the final 20 steps of the chaotic motif was resolved by adding one more qubit. 2. **Fractional-Order Chua's Circuit:** The configured QRC accurately reproduced the complex dynamics of a fractional-order Chua's circuit, correctly capturing nontrivial features like voltage saturation and non-monotonic dynamics. The NMSE for this task reached 10⁻⁴. 3. **FX Market Forecast:** The approach successfully predicted GBP/USD exchange rates, trained on AUD/USD and NZD/USD data. The prediction accuracy was significantly higher (one order of magnitude improvement) than that of classical reservoir computing methods reported in previous studies (NMSE of 10⁻⁵, indicating a relative error of ~0.3%, which is significantly smaller than the daily fluctuations of ~2%). Alternative tests using different combinations of training and testing exchange rate data yielded comparable results. Comparison with ESNs revealed a significant quantum advantage. Even with the number of nodes in ESN increased to 120 (compared to 6 qubits in the quantum model), the quantum model maintained four orders of magnitude higher accuracy in prediction, highlighting its superior transferability. Analysis of quantum correlations (entanglement entropy and tripartite mutual information) during the training process showed that the quantum reservoir transitioned from a scrambled, non-thermal state to a less scrambled, less thermal state, indicating a relationship between quantum correlations and learning power. Experiments with synthetic models that allowed for systematic control of quantum coherence showed that the learning performance increased monotonically with increasing coherence levels, further supporting the role of quantum coherence in the quantum advantage.

The results demonstrate that configured quantum reservoir computing offers a significant improvement over classical reservoir computing methods, particularly in multi-task learning scenarios involving complex dynamical systems and stochastic processes. The superior performance is attributed to the complex quantum dynamics within the reservoir, enabled by quantum coherence. The ability of a single configured quantum reservoir to learn multiple diverse tasks highlights its potential for broader applications in artificial general intelligence. The findings suggest that complex quantum systems, beyond the capabilities of efficient classical simulation, provide valuable computational resources for advanced machine learning applications. The high prediction accuracy achieved in the FX market forecast shows the potential for practical applications in finance.

This research presents a novel approach to quantum reservoir computing that significantly outperforms classical methods in multi-task machine learning. The superior performance, particularly in complex and stochastic systems, is demonstrated across various applications, including gene regulatory networks, fractional-order circuits, and FX market prediction. The quantum advantage is attributed to quantum coherence within the reservoir. Future research could explore the use of larger-scale quantum devices to further enhance performance and investigate applications in other fields.

While the study demonstrates a clear quantum advantage, the number of qubits used (6-8) is relatively small compared to the potential of future quantum computers. The generalizability of the findings to different types of quantum hardware and the scaling behavior with increasing qubit numbers require further investigation. The reliance on a genetic algorithm for optimization may be computationally intensive for very large systems.