Noisy Quantum Kernel Machines

Heyraud, Valentin; Li, Zejian; Denis, Zakari; Boité, Alexandre Le; Ciuti, Cristiano

doi:10.48550/arxiv.2204.12192

Cited by 4 publications

(3 citation statements)

References 41 publications

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“…Quantum kernels stand out as a promising candidate for achieving a practical quantum advantage in data analysis. While there are a number of prior works studying generalization [6][7][8][42][43][44][45][46], only a few discuss the trainability of quantum kernels [8,14,42]. This is largely due to the common belief that the optimal quantum kernel-based model can always be obtained [12][13][14][15] due to the convexity of the problem.…”

Section: Discussionmentioning

confidence: 99%

Exponential concentration and untrainability in quantum kernel methods

Thanasilp

Wang

Cerezo

et al. 2022

Preprint

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Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model's parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from a quantum hardware. In this work we study the trainability of quantum kernels from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value, leading to an exponential scaling of the number of measurements required for successful training. We identify four sources that can lead to concentration including: the expressibility of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation and the trainability of quantum kernel methods.

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Section: Discussionmentioning

confidence: 99%

Exponential concentration and untrainability in quantum kernel methods

Thanasilp

Wang

Cerezo

et al. 2022

Preprint

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“…Another stream of research has emerged on finding a suitable quantum feature map for a given data set with [19] providing a recent review of quantum classification algorithms. Studies on quantum feature maps involve both the study of the kernel function and the study of the quantum circuits which encode the outcome of the kernel function into Hilbert space [20], [21], [22]. A new set of metrics and a protocol has also been proposed to determine the possibility of quantum advantage for a given pair of data set and quantum feature map [23].…”

Section: Introductionmentioning

confidence: 99%

Quantum Kernels for Real-World Predictions Based on Electronic Health Records

Krunic

Flöther

Seegan

et al. 2022

IEEE Trans. Quantum Eng.

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Research on near-term quantum machine learning has explored how classical machine learning algorithms endowed with access to quantum kernels (similarity measures) can outperform their purely classical counterparts. Although theoretical work has shown provable advantage on synthetic data sets, no work done to date has studied empirically whether quantum advantage is attainable and with what data. In this paper, we report the first systematic investigation of empirical quantum advantage (EQA) in healthcare and life sciences and propose an end-to-end framework to study EQA. We selected electronic health records (EHRs) data subsets and created a configuration space of 5-20 features and 200-300 training samples. For each configuration coordinate, we trained classical support vector machine (SVM) models based on radial basis function (RBF) kernels and quantum models with custom kernels using an IBM quantum computer, making this one of the largest quantum machine learning experiments to date. We empirically identified regimes where quantum kernels could provide advantage and introduced a terrain ruggedness index, a metric to help quantitatively estimate how the accuracy of a given model will perform. The generalizable framework introduced here represents a key step towards a priori identification of data sets where quantum advantage could exist.INDEX TERMS artificial intelligence, digital health, electronic health records, empirical quantum advantage, machine learning, quantum kernels, real-world data, small data sets, support vector machines

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“…This has led to proposals and realizations in diverse platforms, including free-space optics [13][14][15], photonics [16,17], nonlinear polariton lattices [18][19][20], memristors [21,22] and beyond [23][24][25][26]. Very recently, such an approach has been explored in a quantum context [27,28], with applications in quantum metrology [29,30], quantum-state control [31][32][33] and image recognition [34,35]. Although it was long thought that a strong nonlinearity of the equations of motion was an essential element of reservoir computing, recent works have shown great performances relying on systems with almost no intrinsic nonlinearity, namely by exploiting the nonlinearity of the measurement [15,36,37] or drawing links with approximate kernel evaluation [38][39][40].…”

mentioning

confidence: 99%

Machine learning via relativity-inspired quantum dynamics

Li,

Heyraud,

Donatella

et al. 2022

Preprint

Self Cite

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We present a machine-learning scheme based on the relativistic dynamics of a quantum system, namely a quantum detector inside a cavity resonator. An equivalent analog model can be realized for example in a circuit QED platform subject to properly modulated driving fields. We consider a reservoir-computing scheme where the input data are embedded in the modulation of the system (equivalent to the acceleration of the relativistic object) and the output data are obtained by linear combinations of measured observables. As an illustrative example, we have simulated such a relativistic quantum machine for a challenging classification task, showing a very large enhancement of the accuracy in the relativistic regime. Using kernel-machine theory, we show that in the relativistic regime the task-independent expressivity is dramatically magnified with respect to the Newtonian regime.

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Noisy Quantum Kernel Machines

Cited by 4 publications

References 41 publications

Exponential concentration and untrainability in quantum kernel methods

Exponential concentration and untrainability in quantum kernel methods

Quantum Kernels for Real-World Predictions Based on Electronic Health Records

Machine learning via relativity-inspired quantum dynamics

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