Machine learning of high dimensional data on a noisy quantum processor

Peters, Evan; Caldeira, João Frois; Ho, Alan L.; Leichenauer, Stefan; Mohseni, Mojtaba; Neven, Hartmut; Spentzouris, P.; Strain, Doug; Perdue, G. N.

doi:10.48550/arxiv.2101.09581

Cited by 15 publications

(20 citation statements)

References 21 publications

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“…The most prominent approach to construct learning models using NISQ devices relies on the use of parametrized quantum circuits (PQCs) [11][12][13][14]. Kernel methods in particular have emerged as one particular candidate to realize QML models [15][16][17][18][19][20][21]. Furthermore, it was recently shown that other types of variational quantum learning models are Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…We also analyze the influence of finite sampling on kernel quality -an issue touched upon in Ref. [21] -showing that the number of samples typically required to achieve an approximation of fixed precision is of third order in the number of datapoints. We review preexisting strategies that can be used to alleviate the influence of noise on the kernel matrix and propose a different one based on a semi-definite program.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Training Quantum Embedding Kernels on Near-Term Quantum Computers

Hubregtsen¹,

Wierichs²,

Gil-Fuster³

et al. 2021

Preprint

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Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space of a quantum computer are a particular quantum kernel technique that allows to gather insights into learning problems and that are particularly suitable for noisy intermediate-scale quantum devices. In this work, we first provide an accessible introduction to quantum embedding kernels and then analyze the practical issues arising when realizing them on a noisy near-term quantum computer. We focus on quantum embedding kernels with variational parameters. These variational parameters are optimized for a given dataset by increasing the kernel-target alignment, a heuristic connected to the achievable classification accuracy. We further show under which conditions noise from device imperfections influences the predicted kernel and provide a strategy to mitigate these detrimental effects which is tailored to quantum embedding kernels. We also address the influence of finite sampling and derive bounds that put guarantees on the quality of the kernel matrix. We illustrate our findings by numerical experiments and tests on actual hardware.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Training Quantum Embedding Kernels on Near-Term Quantum Computers

Hubregtsen¹,

Wierichs²,

Gil-Fuster³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Pioneered experimental explorations have validated the crucial role of ansatz when applying VQAs to accomplish tasks in different fields such as machine learning [30][31][32][33],…”

mentioning

confidence: 99%

Quantum circuit architecture search on a superconducting processor

Linghu¹,

Yang²,

Wang³

et al. 2022

Preprint

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Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale quantum (NISQ) machines. To address this issue, here we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz towards classification tasks. Compared with the heuristic ansätze, the ansatz designed by QAS improves test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansätze. Our work provides concrete guidance for developing variable ansätze to tackle various large-scale quantum learning problems with advantages.

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“…One possible route to quantum advantage in machine learning is the use of quantum embedding kernels [3][4][5], where quantum computers are used to encode data in ways that are difficult for classical machine learning methods [6][7][8]. Noisy intermediate scale quantum computers [9,10] are capable of solving tasks difficult for classical computers [11,12] and have shown promise in running proof-of-principle quantum machine learning applications [13][14][15][16][17][18][19][20][21][22][23]. However, major bottlenecks still limit the use of quantum hardware for machine learning with practical applications.…”

mentioning

confidence: 99%