2020
DOI: 10.3390/e22080828
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Hybrid Quantum-Classical Neural Network for Calculating Ground State Energies of Molecules

Abstract: We present a hybrid quantum-classical neural network that can be trained to perform electronic structure calculation and generate potential energy curves of simple molecules. The method is based on the combination of parameterized quantum circuits and measurements. With unsupervised training, the neural network can generate electronic potential energy curves based on training at certain bond lengths. To demonstrate the power of the proposed new method, we present the results of using the quantum-classical hybr… Show more

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Cited by 33 publications
(25 citation statements)
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“…When the conditions of Theorem 2 are satisfied, then Θ (L) (x, x ) is positive definite and accordingly λ j > 0 holds for all j. Thus in the limit t → ∞, the solution (14) states that f θ(t) (x a ) = y a holds for all a; namely, the value of the cost L C t reaches the global minimum L t = 0. This fine convergence to the global minimum explains why the overparameterized CNN can be successfully trained.…”
Section: Theoremsmentioning
confidence: 92%
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“…When the conditions of Theorem 2 are satisfied, then Θ (L) (x, x ) is positive definite and accordingly λ j > 0 holds for all j. Thus in the limit t → ∞, the solution (14) states that f θ(t) (x a ) = y a holds for all a; namely, the value of the cost L C t reaches the global minimum L t = 0. This fine convergence to the global minimum explains why the overparameterized CNN can be successfully trained.…”
Section: Theoremsmentioning
confidence: 92%
“…If the minimum of the eigenvalues, λ min , is enough larger than 0, the cost function quickly converges to the global minimum in the number of iteration O(1/λ min ). Otherwise, the speed of convergence is not determined only by the spectrum of the eigenvalues, but the other factors in (14) need to be taken into account; actually many of the reasonable settings correspond to this case [20], and thus we will consider this setting in the following.…”
Section: E When May Cnn Fail?mentioning
confidence: 99%
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“…An alternative approach is to apply the hybrid quantum-classical scheme and measure the outputs at the end of each layer, so that the correlation can be eliminated. Such a hybrid quantum-classical scheme has been widely used in quantum machine learning 29,[51][52][53][54] . In the following texts, we will discuss how to apply U-LRY in the hybrid quantum-classical scheme and analyze its cost complexity.…”
Section: Methodsmentioning
confidence: 99%
“…In large part, quantum machine learning research has recently been centered around the use of variational quantum algorithms as machine learning models 14 17 due to their high expressibility and rapid trainability compared to classical networks 17 . Extensive research has also been done at the intersection of classical and quantum machine learning to create hybrid machine learning techniques 18 – 20 , as well as in techniques for training quantum neural networks 21 and in machine learning using quantum-enhanced feature spaces 22 .…”
Section: Introductionmentioning
confidence: 99%