Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree–Fock

Tamayo-Mendoza, Teresa; Kreisbeck, Christoph; Lindh, Roland; Aspuru‐Guzik, Alán

doi:10.1021/acscentsci.7b00586

Cited by 79 publications

(83 citation statements)

References 69 publications

(155 reference statements)

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“…It is rather encouraging that with moderate effort one can reach the state-of-the-art performance in variational optimizing iPEPS [34,35]. The success is also a nontrivial demonstration that one can indeed stabilize reverse mode automatic differentiation for linear algebra operations appeared in scientific computation [47].…”

Section: B Gradient Based Optimization Of Ipepsmentioning

confidence: 87%

“…Automatic differentiation is the computational engine of modern deep learning applications [43,44]. Moreover, automatic differentiation also finds applications in quantum optimal control [45] and quantum chemistry calculations such as computing forces [46] and optimizing basis parameters [47].…”

Section: A Automatic Differentiationmentioning

confidence: 99%

“…The appearance of the eigenvalue difference in the denominator of F is a reminder of the first order nondegenerate perturbation theory. Reference [47] concerned about the stability of the backward through the eigensolver, thus turned to less efficient forward mode automatic differentiation for variational optimization of Hartree-Fock basis. Actually in many physical problems the final object function depends on part of the eigenvalues and eigenstates in a gauge independent way, e.g., a quadratic form of occupied eigenstates.…”

Section: Symmetric Eigensolvermentioning

confidence: 99%

“…Backpropagating through the whole TRG procedure, and in particular the SVD, allows one to compute physical observables using higher order derivatives. It is remarkable that this works at all given many of the degenerate singular values due to the Z 2 symmetry of the Ising model [47]. To obtain correct physical results, it is crucial to implement the SVD backward function in a numerical stable way as explained in Sec.…”

Section: Applicationsmentioning

confidence: 99%

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Differentiable Programming Tensor Networks

et al. 2019

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Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation. The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using automatic differentiation. We present essential techniques to differentiate through the tensor networks contraction algorithms, including numerical stable differentiation for tensor decompositions and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications. * wanglei@iphy.ac.cn † txiang@iphy.ac.cn This fact has limited broad adoption of the gradient based optimization of tensor network states to more complex systems. Alternative approaches, such as computing the gradient using numerical derivative has limited accuracy and efficiency, therefore only applies to cases with few variational parameters [36,37]. While deriving the gradient manually using the chain rule is only manageable for purposely designed simple tensor network structures [38].Differentiable programming provides an elegant and efficient solution to these problems by composing the whole tensor network program in a fully differentiable manner. In this paper, we present essential automatic differentiation techniques which compute (higher order) derivatives of tensor network programs efficiently to numeric precision. This progress opens the door to gradient-based (and even Hessian-based) optimization of tensor network states in a general setting. Moreover, computing (higher order) gradients of the output of a tensor network algorithm offer a straightforward approach to compute physical quantities such as the specific heat and magnetic susceptibilities. The differentiable programming approach is agnostic to the detailed lattice geometry, Hamiltonian, and tensor network contraction schemes. Therefore, the approach is general enough to support a wide class of tensor network applications.We will focus on applications which involve two dimensional infinite tensor networks where the differentiable programming techniques offer significant benefits compared to the conventional approaches. We show that after solving m...

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Section: B Gradient Based Optimization Of Ipepsmentioning

confidence: 87%

Section: A Automatic Differentiationmentioning

confidence: 99%

Section: Symmetric Eigensolvermentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

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Differentiable Programming Tensor Networks

et al. 2019

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“… 16 Yang and Gao and co-workers employ Bayesian learning and variational optimization to determine the reaction coordinate for an in-water (retro-)Claisen rearrangement, 17 Pentelute and co-workers use random forest classifiers to predict cell-penetrating peptides to deliver therapeutics, 18 and Aspuru-Guzik and co-workers apply automatic differentiation to compute derivatives in quantum chemical calculations. 19 In Center Stage , Neil Savage interviews Alán Aspuru-Guzik about quantum computing, machine learning, and open access. 20 In First Reactions Sánchez-Lengeling and Aspuru-Guzik discuss how to train machines to possess chemical intuition.…”

mentioning

confidence: 99%