Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus

Holmes, Zoë; Sharma, Kunal; Cerezo, M.; Coles, Patrick J.

doi:10.1103/prxquantum.3.010313

Cited by 286 publications

(236 citation statements)

References 34 publications

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“…It has also been noticed that highly expressive ansatzes are more difficult to train [22,32,39], which is the same with classical machine learning. Various strategies [35,17,30,19] have been proposed to improve VQA trainability.…”

Section: Related Workmentioning

confidence: 77%

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Wang

et al. 2021

Preprint

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Variational quantum algorithms are the quantum analogy of the successful neural network in classical machine learning. The ansatz architecture design, which is similar to classical neural network architecture design, is critical to the performance of a variational quantum algorithm. In this paper, we explore how to design efficient ansatz and investigate several common design options in today's quantum software frameworks. In particular, we study the number of effective parameters in different ansatz architectures and theoretically prove that an ansatz with parameterized RX and RZ gates and alternating two-qubit gate entanglement layers would be more efficient (i.e., more effective parameters per two-qubit gate). Such ansatzes are expected to have stronger expressive power and obtain better solutions. Numerical experimental results show that our efficient ansatz architecture outperforms other ansatzes with smaller ansatz size and better optimization results.

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Section: Related Workmentioning

confidence: 77%

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Wang

et al. 2021

Preprint

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“…the investigation of different cost functions such that the occurrence of barren plateaus can be avoided [93]. Moreover, it is a challenge to find suitable variational ansätze that are sufficiently expressive while avoiding the occurrence of barren plateaus [94]. Eventually, one aims at finding hardware-specific ansätze that allow for an easy application of a QNN on available quantum hardware and do not suffer from serious trainability problems.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantum Error Correction with Quantum Autoencoders

Locher¹,

Cardarelli²,

Müller³

2022

Preprint

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Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction. Specifically, we demonstrate how quantum neural networks, in the form of quantum autoencoders, can be trained to learn optimal strategies for active detection and correction of errors, including spatially correlated computational errors as well as qubit losses. We highlight that the denoising capabilities of quantum autoencoders are not limited to the protection of specific states but extend to the entire logical codespace. We also show that quantum neural networks can be used to discover new logical encodings that are optimally adapted to the underlying noise. Moreover, we find that, even in the presence of moderate noise in the quantum autoencoders themselves, they may still be successfully used to perform beneficial quantum error correction.

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“…Furthermore, there exist limitations of barren plateaus in deep PQC-based algorithms, as initially realised in [19]. Here, the exponential suppression of gradient with increasing depth of circuit, has also been shown to be linked to the expressibility of PQCs [20]. In addition to barren plateaus, PQCs are seen to exhibit narrow gorges [21] which is the occurrence of the existence of cost landscape minima in narrow wells that get steeper with increasing depth.…”

Section: Introductionmentioning

confidence: 94%

Clustering and enhanced classification using a hybrid quantum autoencoder

Srikumar,

Hill,

Hollenberg

2021

Preprint

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Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify -and classically represent -their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states -which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

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Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus

Cited by 286 publications

References 34 publications

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms

Quantum Error Correction with Quantum Autoencoders

Clustering and enhanced classification using a hybrid quantum autoencoder

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