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arXiv:2108.12131 · Physical Review Applied

Quantum Extreme Reservoir Computation Utilizing Scale-Free Networks

Akitada Sakurai, Marta P. Estarellas, William J. Munro, Kae Nemoto

Published Jun 23, 2022• 35 citations
arXivHTMLPDF

Abstract

Today's quantum processors composed of fifty or more qubits have allowed us to enter a computational era where the output results are not easily simulatable on the world's biggest supercomputers. What we have not seen yet, however, is whether or not the complexity achievable with such quantum processors would ever be useful for any practical applications. In the quantum neural network approach, there has been an expectation that the Hilbert space can serve as a computational resource by providing a large feature space; however, it is not understood, nor illustrated in what way the Hilbert space provides that computational power. In this work we introduce a resource-efficient quantum neural network model with a focus on the role of the feature space the quantum processors can give. Then we apply it for classification tasks, showing a quantum advantage in terms of the physical resources needed to realize the neural network. To facilitate the Hilbert space as a large feature space, we utilize scale-free networks that can be generated in a discrete-time crystal model. The virtue of this approach is in both its theoretical simplicity and its practical applicability: our quantum neural network model is simple enough to identify the role of the Hilbert space as the feature space, and, furthermore, can be implemented with current technology. Our model does not require optimization of the quantum processor, and hence once the quantum processor has been set, it can be used for other different classification problems without any changes in the quantum processor itself.

DOI
10.1103/physrevapplied.17.064044

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Today's quantum processors composed of fifty or more qubits have allowed us to enter a computational era where the output results are not easily simulatable on the world's biggest supercomputers. What we have not seen yet, however, is whether or not the complexity achievable with such quantum processors would ever be useful for any practical applications. In the quantum neural network approach, there has been an expectation that the Hilbert space can serve as a computational resource by providing a large feature space; however, it is not understood, nor illustrated in what way the Hilbert space provides that computational power. In this work we introduce a resource-efficient quantum neural network model with a focus on the role of the feature space the quantum processors can give. Then we apply it for classification tasks, showing a quantum advantage in terms of the physical resources needed to realize the neural network. To facilitate the Hilbert space as a large feature space, we utilize scale-free networks that can be generated in a discrete-time crystal model. The virtue of this approach is in both its theoretical simplicity and its practical applicability: our quantum neural network model is simple enough to identify the role of the Hilbert space as the feature space, and, furthermore, can be implemented with current technology. Our model does not require optimization of the quantum processor, and hence once the quantum processor has been set, it can be used for other different classification problems without any changes in the quantum processor itself.
The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum reservoir (feature space) that does not need to be optimized for different problem instances. Originally, a periodically driven system Hamiltonian dynamics was employed as the quantum feature map. In this work we capture how the quantum feature map is generated as the number of time-steps of the dynamics increases by a method to characterize unitary matrices in the form of weighted networks. Furthermore, to identify the key properties of the feature map that has sufficiently grown, we evaluate it with various weighted network models that could be used for the quantum reservoir in image classification situations. At last, we show how a simple Hamiltonian model based on a disordered discrete time crystal with its simple implementation route provides nearly optimal performance while removing the necessity of programming of the quantum processor gate by gate.
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core challenge in understanding, implementing and ultimately using quantum neural networks is that they represent many-body systems with an exponentially large Hilbert space, in combination with a large parameter search space. Moreover, noise -- which is inherent to any quantum measurement -- sets practical limits for the estimation of training loss. Here, we study physics-informed large-scale quantum neural networks that are trained through a finite number of noisy loss function measurements. We show that this architecture permits the construction of nontrivial decision boundaries that enable the classification of quantum states through measuring an order parameter. Our approach can directly process quantum data that is output from quantum simulators and computers and is well suited for implementation on current hardware. Moreover, owed to a close link between the neural network dynamics and the evolution of Markovian open many-body quantum systems, one may expect a certain robustness to noise, which is ubiquitous in the current NISQ era.
Quantum reservoir computing is a machine-learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output features measured from the quantum system. Various implementations of quantum reservoir computing have been explored in simulations, with different measured features. Although simulations have shown that quantum reservoirs present advantages in performance compared to classical reservoirs, experimental implementations have remained scarce. This is due to the challenge of obtaining a large number of output features that are nonlinear transformations of the input data. In this work, we show that even with a circuit quantum electrodynamics system as simple as a single transmon coupled to a readout resonator, we can implement a proof-of-concept realization of quantum reservoir computing. We obtain a large number of nonlinear features from a single physical system by encoding the input data in the amplitude of a coherent drive and measuring the cavity state in the Fock basis. We demonstrate classification of two classical tasks with significantly smaller hardware resources and fewer measured features compared to classical neural networks. Our experimental results are supported by numerical simulations that show additional Kerr nonlinearity is beneficial to reservoir performance. Our work demonstrates a hardware-efficient quantum neural-network implementation that can be further scaled up and generalized to other quantum machine-learning models.
Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the preparation of multiple copies of the same quantum state to generate the nonlinearity, with the copy number increasing significantly for highly oscillating functions, resulting in a huge demand for a large-scale quantum processor. To address this problem, we propose a new QNN model that harbors universality without the need of multiple state-duplications, and is more likely to get implemented on near-term devices. To demonstrate the effectiveness, we compare our proposal with two popular QNN models in solving typical supervised learning problems. We find that our model requires significantly fewer qubits and it outperforms the other two in terms of accuracy and relative error.
Reservoir computing leverages rich, non-linear dynamics to process temporal data. Quantum variants promise enhanced expressivity from high-dimensional Hilbert spaces, yet their practical applicability is hindered by hardware noise and concentration effects that can erase input-output distinguishability at large system sizes. In this work, we present and experimentally demonstrate a Quantum Extreme Learning Machine (QELM) tailored to state-of-the-art superconducting platforms, employing up to 124 qubits and circuits with more than 5,000 two-qubit gates on IBM Quantum computers. We introduce a practical multi-objective hyperparameter tuning strategy that jointly monitors observable variability, capacity, and task performance to identify noise-robust operating points. In addition, we develop a local eigentask analysis that enables computationally efficient feature selection and effective information retrieval. We report evidence of a regime of optimality that is identifiable at small scales and transferable across tasks and larger systems, and we achieve performances competitive with leading classical baselines on representative benchmarks for time-series forecasting and satellite image classification. Together, our results establish a viable and robust framework for large-scale, pre-fault-tolerant quantum machine learning and provide a foundation for extending reservoir-based methods to more expressive architectures and real-world scenarios.
Many recent machine learning tasks resort to quantum computing to improve classification accuracy and training efficiency by taking advantage of quantum mechanics, known as quantum machine learning (QML). The variational quantum circuit (VQC) is frequently utilized to build a quantum neural network (QNN), which is a counterpart to the conventional neural network. Due to hardware limitations, however, current quantum devices only allow one to use few qubits to represent data and perform simple quantum computations. The limited quantum resource on a single quantum device degrades the data usage and limits the scale of the quantum circuits, preventing quantum advantage to some extent. To alleviate this constraint, we propose an approach to implementing a scalable quantum neural network (SQNN) by utilizing the quantum resource of multiple small-size quantum devices cooperatively. In an SQNN system, several quantum devices are used as quantum feature extractors, extracting local features from an input instance in parallel, and a quantum device works as a quantum predictor, performing prediction over the local features collected through classical communication channels. The quantum feature extractors in the SQNN system are independent of each other, so one can flexibly use quantum devices of varying sizes, with larger quantum devices extracting more local features. Especially, the SQNN can be performed on a single quantum device in a modular fashion. Our work is exploratory and carried out on a quantum system simulator using the TensorFlow Quantum library. The evaluation conducts a binary classification on the MNIST dataset. It shows that the SQNN model achieves a comparable classification accuracy to a regular QNN model of the same scale. Furthermore, it demonstrates that the SQNN model with more quantum resources can significantly improve classification accuracy.