Quantum Semantic Learning by Reverse Annealing of an Adiabatic Quantum Computer

Rocutto, Lorenzo; Destri, C.; Prati, Enrico

doi:10.1002/qute.202000133

Cited by 39 publications

(26 citation statements)

References 33 publications

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“…Within the field of quantum machine learning (QML) [6,7], if one neglects the implementation of quantum neural networks on adiabatic quantum computers [8], there are essentially two kind of proposals of quantum neural networks on a gate-model quantum computer. The first consists of defining a quantum neural network as a variational quantum circuit composed of parameterized gates, where non-linearity is introduced by measurements operations [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Quantum activation functions for quantum neural networks

Maronese¹,

Destri²,

Prati³

2022

Preprint

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The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement-based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik's theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.

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Section: Introductionmentioning

confidence: 99%

“…Instead, differently from both the above proposals and from quantum annealing based algorithms applied to neural networks [8], we develop a fully reversible algorithm.…”

Section: Introductionmentioning

confidence: 99%

Quantum activation functions for quantum neural networks

Maronese¹,

Destri²,

Prati³

2022

Preprint

Self Cite

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“…Dymtro et al [26] performed a benchmarking study, to show that for harder problems Boltzmann machines trained using quantum annealing gives better gradients as compared to CD. Lorenzo et al [27] used RBM trained with reverse annealing to carry out semantic learning that achieved good scores on reconstruction tasks. Koshka et al [28] showed D-Wave quantum annealing performed better than classical simulated annealing for RBM training when the number of local valleys on the energy landscape was large.…”

Section: Introductionmentioning

confidence: 99%

“…The term epoch means a full cycle of iterations, with each training pattern participating only once. Accuracy is defined as:AccuracyNumber of correct predictions Total number of predictions(27)…”

mentioning

confidence: 99%

Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer

et al. 2021

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Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit “bars and stripes” dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD.

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“…Moreover, one can also iterate the process, leading to a strategy known as iterated reverse annealing [12,26]. We note that there is some evidence that reverse annealing can outperform forward annealing in solving optimization problems [26][27][28][29][30][31][32][33]. However, our focus in this work is not on algorithmic performance, but rather on using the rich playground provided by the p = 2 p-spin model under reverse annealing to answer the question of which of a variety of models best describes the results obtained from the D-Wave annealer.…”

Section: Introductionmentioning

confidence: 99%

Breakdown of the weak coupling limit in quantum annealing

Bando,

Yip,

Chen

et al. 2021

Preprint

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Reverse annealing is a variant of quantum annealing, in which the system is prepared in a classical state, reverse-annealed to an inversion point, and then forward-annealed. We report on reverse annealing experiments using the D-Wave 2000Q device, with a focus on the p = 2 p-spin problem, which undergoes a second order quantum phase transition with a gap that closes polynomially in the number of spins. We concentrate on the total and partial success probabilities, the latter being the probabilities of finding each of two degenerate ground states of all spins up or all spins down, the former being their sum. The empirical partial success probabilities exhibit a strong asymmetry between the two degenerate ground states, depending on the initial state of the reverse anneal. To explain these results, we perform open-system simulations using master equations in the limits of weak and strong coupling to the bath. The former, known as the adiabatic master equation (AME), with decoherence in the instantaneous energy eigenbasis, predicts perfect symmetry between the two degenerate ground states, thus failing to agree with the experiment. In contrast, the latter, known as the polaron transformed Redfield equation (PTRE), is in close agreement with experiment. The same is true for a purely classical model known as spin-vector Monte Carlo with transverse-fielddependent updates (SVMC-TF). Thus our results present a strong challenge to the sufficiency of the weak system-bath coupling limit in describing the dynamics of current experimental quantum annealers, at least for annealing on timescales of a µsec or longer.

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Quantum Semantic Learning by Reverse Annealing of an Adiabatic Quantum Computer

Cited by 39 publications

References 33 publications

Quantum activation functions for quantum neural networks

Quantum activation functions for quantum neural networks

Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer

Breakdown of the weak coupling limit in quantum annealing

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