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Natural quantum reservoir computing for temporal information processing

Yudai Suzuki, Qi Gao, Ken C. Pradel, Kenji Yasuoka, Naoki Yamamoto

arXiv:2107.05808v2quant-ph

TL;DR

Temporal information processing often uses recurrent neural networks, whose training is computationally demanding. This paper uses natural noise in superconducting quantum processors as reservoir dynamics and reports better performance than linear models on some benchmark and classification tasks.

  • Problem

    Recurrent neural networks are often used for temporal information processing, but their recurrent training is computationally demanding.

    Source: Natural quantum reservoir · p. 1

  • Method

    The framework uses intrinsic noise in superconducting quantum processors to provide dissipative dynamics for a quantum reservoir.

    Source: Natural quantum reservoir · p. 2

  • Results

    The proposed scheme outperformed linear regression or classification models on some NARMA and object-classification tasks.

    Source: Conclusion · p. 13

  • Takeaways & Limitations

    The results indicate that noise in currently available quantum devices can serve as a potentially rich computational resource for reservoir computing.

    Source: Conclusion · p. 13

    Improving performance and processing speed remains necessary, and the device noise mechanisms need to be better identified to guide reservoir design.

    Source: Conclusion · p. 13

Abstract

from arXiv · show

Reservoir computing is a temporal information processing system that exploits artificial or physical dissipative dynamics to learn a dynamical system and generate the target time-series. This paper proposes the use of real superconducting quantum computing devices as the reservoir, where the dissipative property is served by the natural noise added to the quantum bits. The performance of this natural quantum reservoir is demonstrated in a benchmark time-series regression problem and a practical problem classifying different objects based on temporal sensor data. In both cases the proposed reservoir computer shows a higher performance than a linear regression or classification model. The results indicate that a noisy quantum device potentially functions as a reservoir computer, and notably, the quantum noise, which is undesirable in the conventional quantum computation, can be used as a rich computation resource.

Natural quantum reservoir

The section motivates reservoir computing as a lower-cost alternative to recurrent training for temporal tasks, then proposes noisy superconducting processors as reservoirs and reports comparative gains on two tasks.

Natural quantum reservoir

  • Recurrent neural networks are commonly used for temporal information processing, but recurrently connecting nodes to approximate a target dynamical system is computationally demanding.Source: Natural quantum reservoir · p. 1
  • Reservoir computing maps temporal inputs to high-dimensional dynamical states and trains a linear readout, enabling faster, more stable learning at lower cost than typical recurrent networks.Source: Natural quantum reservoir · p. 1
  • Physical reservoirs range from FPGAs and robots to quantum systems, whose complex dynamics are conjectured to benefit some temporal tasks; implementations include NMR systems and superconducting processors.Source: Natural quantum reservoir · pp. 1–2
  • The proposed framework uses intrinsic noise in gate-based superconducting processors to provide dissipative reservoir dynamics, unlike artificial reservoirs with an available mathematical model.Here, a natural reservoir is a physical system difficult to describe mathematically.Source: Natural quantum reservoir · p. 2
  • The Melbourne quantum reservoir outperformed linear regression on NARMA tasks, while the Toronto reservoir beat a linear classifier on three-object classification.The object-classification task used sensor data gathered by grabbing the objects.Source: Natural quantum reservoir · p. 2

Methods

Reservoir computing fixes the reservoir dynamics and trains a readout, while quantum reservoir computing represents those dynamics with input-dependent maps on a density operator. Here, the proposed device-specific reservoir uses natural hardware noise and measured qubit observables.

General framework of reservoir computing.

  • In reservoir computing, fixed dynamics map inputs to states, while training adjusts a linear readout to approximate the target output.Feature extraction is therefore left to the reservoir dynamics, making reservoir choice and design important.Source: General framework of reservoir computing · p. 2
  • Readout weights are supervised by minimizing training-phase mean squared error, which the paper says can be solved using linear regression and a pseudoinverse.The training sequence is assembled from observed reservoir features with a bias term.Source: General framework of reservoir computing · p. 2

Quantum reservoir computing model.

  • The quantum reservoir evolves a density operator through an input-dependent CPTP map, with the input encoded on an ancillary qubit in the cited artificial QRC construction.Tracing out that ancillary qubit is essential to that construction's dissipative property.Source: Quantum reservoir computing model · pp. 2–3
  • Readout uses local-observable expectation values, including each qubit's Pauli Z value, measured with 8192 shots per timestep.The circuit begins in the |+⟩ state and is repeatedly applied to obtain the output signal.Source: Quantum reservoir computing model · pp. 3–4, Figure 2 · p. 4
  • The proposed natural quantum reservoir uses hardware noise as a computational resource, unlike artificial QRC's ancillary-qubit trace used to create dissipation.The paper notes that depolarizing error can provide convergence toward a stable state and that noisy devices may exhibit temporal memory.Source: Quantum reservoir computing model · p. 3
  • The proposed device model applies input-dependent unitary operations alongside the real device's unmodeled CPTP map.The restricted local two-qubit gate is chosen to test whether natural noise enriches the dynamics rather than relying on a richer unitary.Source: Quantum reservoir computing model · p. 3

Results and discussion

The experiments evaluate natural quantum reservoirs on NARMA time-series regression and sensor-based object classification using IBM Melbourne and Toronto devices. Performance varies by device and task: the QR systems outperform linear models on some tasks, but not all.

Results and discussion / NARMA task.

  • The NARMA evaluation uses orders 2, 5, and 10 to assess nonlinearity, with 10 washout, 70 training, and 20 testing timesteps from 100-step sequences.The experiments used Melbourne and Toronto processors with circuit-transpiler optimization level zero.Source: NARMA task · pp. 4–5, Results and discussion · p. 4

NARMA task. / Object classification task.

  • Across NARMA, Melbourne QR beats LR on NARMA2 and NARMA5, but neither device beats LR on NARMA10; classification QR beats the linear model on A-vs-C and three-class tasks, not A-vs-B.For three-class classification, QR accuracy is almost 0.3 higher than the linear model.Source: Table 1 · p. 6, NARMA task · p. 7, Table 3 · p. 11

NARMA task.

  • Melbourne output means remain relatively close across training and testing, whereas Toronto shows mean gaps for some qubits; performance depends on device, and Toronto improves with system size across NARMA tasks.The authors suggest device output-signal stationarity and noise-related higher-order time series may help explain these differences.Source: NARMA task · pp. 7, 9, Figure 6 · p. 7, Figure 7 · p. 8
  • Against ESNs, Melbourne QR is comparable to an optimal 2-node model but inferior to an arbitrary 5-node model, while Toronto is worse than an arbitrary 2-node model.The authors describe their QR scheme as oversimplified for these tasks and identify gate sets and input injection as possible tuning parameters.Source: NARMA task · p. 9

Object classification task.

  • Object classification used sensor time series from three objects, with 20 samples per object from 25 grabbing cycles and 10-fold cross-validation on Toronto's four-subsystem QR.The three objects were an ABS LEGO cube, a PLA cube, and a PLA sphere; each sample contained 90 timesteps, with the first 40 discarded for washout.Source: Object classification task · pp. 9, 12, Figure 8 · p. 10

Conclusion

The proposed QRC uses intrinsic quantum noise as a computational resource and outperforms linear models on some NARMA and classification tasks. The conclusion identifies performance and speed improvements, noise characterization, and processor design as remaining directions.

  • The proposed QRC leverages intrinsic quantum noise as a computational resource and outperforms linear regression or classification models for some NARMA and classification tasks.Source: Conclusion · p. 13
  • Improving performance and processing speed requires investigating device noise mechanisms and their controllability.The authors point to system-identification methods for complex noise, including crosstalk, as a way to inform reservoir configurations.Source: Conclusion · p. 13
  • Experiments require LS circuit runs to generate output signals, making processing time-consuming; mid-circuit measurements can reduce this to S runs on IBM processors.Source: Conclusion · p. 13
  • The scheme is not limited to NISQ devices, and future work includes exploring noise levels, noise dynamics, and processors specialized for QRC.The authors note that noise could be introduced in fault-tolerant devices by relaxing qubit control.Source: Conclusion · p. 13
  • The manuscript was received on 24 August 2021 and accepted on 28 December 2021.Source: Conclusion · p. 13

Additional information

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