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Scientific Reports

Taking advantage of noise in quantum reservoir computing

Laia Domingo, Gabriel G. Carlo, F. Borondo

Published May 31, 2023• 55 citations
Publisher

Abstract

The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware.

DOI
10.1038/s41598-023-35461-5

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Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing, Scientific Reports, 13:8790, 2023] suggests that certain channels can, in appropriate regimes, improve performance by enriching the reservoir's effective dynamics. Motivated by this idea we propose a geometric mechanism to explain how non-unital noise applied together with a universal gate set leads to a faster approach to Haar-like distributions of the final states. We find that noise of this kind induces an effective volume expansion on the manifold of pure states. In order to intuitively understand this we use a minimal 1 qubit model where we take the amplitude damping channel and combine it with a renormalization rule that associates to each resulting mixed state a representative pure state. This composition defines a globally expanding nonlinear map on the space of pure states. We analytically derive the local area expansion factor and identify the global expansion threshold. Finally, we combine amplitude damping with the G3 = {H, T, CNOT} universal gate set to show how the approach to Haar-like behavior is faster in an appropriate parameter region. This leads us to propose noise as a possible resource in future quantum algorithms.

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The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware.
The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware.
Abstract Quantum machine learning (QML) is an emerging field with significant potential, yet it remains highly susceptible to noise, which poses a major challenge to its practical implementation. While various noise mitigation strategies have been proposed to enhance algorithmic performance, the impact of noise is not fully understood. In this work, we investigate the effects of amplitude and phase damping noise on a quantum reinforcement learning algorithm. Through analytical and numerical analysis, we assess how these noise sources influence the learning process and overall performance. Our findings contribute to a deeper understanding of the role of noise in quantum learning algorithms and suggest that, rather than being purely detrimental, unavoidable noise may present opportunities to enhance QML processes.
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing and develop state-of-the-art variants capable of addressing diverse applications in machine learning. The research demonstrates the algorithm's robustness and adaptability across very different domains, including agricultural time series forecasting and the time propagation of quantum systems. The first contribution of this thesis consists in developing a reservoir computing-based methodology to predict future agricultural product prices, which is crucial for ensuring the sustainability of the food market. The next contribution of the thesis is devoted to solving the Schrödinger equation for complex quantum systems. A novel reservoir computing framework is proposed to efficiently propagate quantum wavefunctions in time, enabling the computation of all eigenstates of a quantum system within a specific energy range. This approach is used to study prominent systems in the field of quantum chemistry and quantum chaos. The last contribution of this thesis focuses on optimizing algorithm designs for quantum reservoir computing. The results demonstrate that families of quantum circuits with higher complexity, according to the majorization criterion, yield superior performance in quantum machine learning. Moreover, the impact of quantum noise on the algorithm performance is evaluated, revealing that the amplitude damping noise can actually be beneficial for the performance of quantum reservoir computing, while the depolarizing and phase damping noise should be prioritized for correction. Furthermore, the optimal design of quantum reservoirs is employed to construct a hybrid quantum-classical neural network that tackles a fundamental problem in drug design.
Quantum machine learning (QML) holds significant promise for accelerating and enhancing machine learning tasks. However, the inherent fragility of quantum systems to noise poses a substantial challenge to the successful implementation of QML algorithms. This paper investigates and proposes novel noise optimization strategies specifically tailored for QML. The core claim is to design a strategy capable of effectively handling noise within QML algorithms, ultimately boosting model training accuracy and robustness. The proposed mechanism leverages either the quantum decoherence principle to suppress noise or quantum entanglement mechanisms to mitigate its effects. We explore various approaches, focusing on adaptive noise mitigation techniques and incorporating error correction methodologies within the quantum computation framework. The presented framework aims to improve the reliability of QML algorithms and contribute to the development of practical, robust quantum machine learning systems. The research addresses a critical gap in the field by offering a systematic approach to noise management in QML, a crucial step towards realizing the full potential of this technology. The ultimate goal is to demonstrate that, with appropriate noise optimization, QML algorithms can achieve performance comparable to, or exceeding, classical machine learning algorithms.
Quantum computing has been moving from a theoretical phase to practical one, presenting daunting challenges in implementing physical qubits, which are subjected to noises from the surrounding environment. These quantum noises are ubiquitous in quantum devices and generate adverse effects in the quantum computational model, leading to extensive research on their correction and mitigation techniques. But do these quantum noises always provide disadvantages? We tackle this issue by proposing a framework called quantum noise-induced reservoir computing and show that some abstract quantum noise models can induce useful information processing capabilities for temporal input data. We demonstrate this ability in several typical benchmarks and investigate the information processing capacity to clarify the framework's processing mechanism and memory profile. We verified our perspective by implementing the framework in a number of IBM quantum processors and obtained similar characteristic memory profiles with model analyses. As a surprising result, information processing capacity increased with quantum devices' higher noise levels and error rates. Our study opens up a novel path for diverting useful information from quantum computer noises into a more sophisticated information processor.
Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing, Scientific Reports, 13:8790, 2023] suggests that certain channels can, in appropriate regimes, improve performance by enriching the reservoir's effective dynamics. Motivated by this idea we propose a geometric mechanism to explain how non-unital noise applied together with a universal gate set leads to a faster approach to Haar-like distributions of the final states. We find that noise of this kind induces an effective volume expansion on the manifold of pure states. In order to intuitively understand this we use a minimal 1 qubit model where we take the amplitude damping channel and combine it with a renormalization rule that associates to each resulting mixed state a representative pure state. This composition defines a globally expanding nonlinear map on the space of pure states. We analytically derive the local area expansion factor and identify the global expansion threshold. Finally, we combine amplitude damping with the G3 = {H, T, CNOT} universal gate set to show how the approach to Haar-like behavior is faster in an appropriate parameter region. This leads us to propose noise as a possible resource in future quantum algorithms.