Fermionic neural-network states for ab-initio electronic structure

Choo, Kenny; Mezzacapo, Antonio; Carleo, Giuseppe

doi:10.1038/s41467-020-15724-9

Cited by 207 publications

(197 citation statements)

References 43 publications

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“…Nagai et al 8 showed that accurate densities of just three small molecules are sufficient to create machine-learned approximations that are comparable to those created by people. In ab initio quantum chemistry, Welborn et al 9 have shown how to use features from Hartree-Fock calculations to accurately predict CCSD energies, while an intriguing alternative is to map to spin problems and use a restricted Boltzmann machine 10 . In the last year, two new applications for finding wavefunctions within QMC have appeared 11,12 .…”

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confidence: 99%

Retrospective on a decade of machine learning for chemical discovery

2020

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Over the last decade, we have witnessed the emergence of ever more machine learning applications in all aspects of the chemical sciences. Here, we highlight specific achievements of machine learning models in the field of computational chemistry by considering selected studies of electronic structure, interatomic potentials, and chemical compound space in chronological order. Accurate solutions of the Schrödinger equation for the electrons in molecules and materials would vastly enhance our capability for chemical discovery, but computational cost makes this prohibitive. Since Dirac first exhorted us to find suitable approximations to bypass this cost 1 , much progress has been made, but much remains out of reach for the foreseeable future. The central promise of machine learning (ML) is that, by exploiting statistical learning of the properties of a few cases, we might leapfrog over the worst bottlenecks in this process. As visible from the publication record in the field (Fig. 1), over the decade since Nature Communications first appeared, machine learning has gained increasing traction in the hard sciences 2 , and has found many applications in atomistic simulation sciences 3. Here, we focus on the progress achieved in the last decade on three interrelated topics (i) electronic structure theory, broadly defined, (ii) universal force field models, as used for vibrational analysis or molecular dynamics applications, and (iii) first principles-based approaches enabling the exploration of chemical compound space. Basic challenges The central challenge of Schrödinger space is to use supervised learning from examples to find patterns that either accelerate or improve upon the existing human algorithms behind these technologies. In density functional theory (KS-DFT), this most often means improved approximate functionals; in quantum Monte Carlo (QMC), this is faster ways to find variational wavefunctions; in ab initio quantum chemistry such as coupled cluster considering single, double, and perturbative triple excitations (CCSD(T)), this is learned predictions of wavefunction amplitudes instead of recalculation for every system. In the condensed phase, molecular dynamics simulations yield a vast amount of useful thermodynamic and kinetic properties. Classical force fields cost little to run, but are often accurate only around the equilibrium. The only first-principles alternative is Kohn-Sham density functional theory (DFT), but its computational cost vastly reduces what is practical. A central challenge of configuration space is therefore to produce energies and forces from a classical

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confidence: 99%

Retrospective on a decade of machine learning for chemical discovery

2020

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“…To enhance the computational efficiency of the RBM, the QRBM model are proposed [11,12,13]. Different from the RBM, the QRBM utilizes a quantum circuit to parallelly compute the amplitudes Ψ v (θ), and naturally outputs the superposition state |Ψ(θ)…”

Section: Methodsmentioning

confidence: 99%

“…Zhang et al [12] proposed a variational quantum algorithm to efficiently train the QRBM, where the proposed algorithm reduced the required ancillary qubits. Recently, Carleo et al [13] presented an extension of quantum neural network to model interacting fermionic problems, and Kerstin et al [22] indicated that the Deep QRBM can implement the universal quantum computation tasks. The previous works show outstanding performance in some notable cases of physical interest that are difficult for classical RBM.…”

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confidence: 99%

Quantum restricted Boltzmann machine is universal for quantum computation

Wu¹,

Wei²,

Qin³

et al. 2020

Preprint

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The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the many-body wave functions with high complexity. Quantum neural network provides a powerful tool to represent the large-scale wave function, which has aroused widespread concerns in the quantum superiority era. A significant open problem is what exactly the representational power boundary of the single-layer quantum neural network is. In this paper, we design a 2-local Hamiltonian and then give a kind of Quantum Restricted Boltzmann Machine (QRBM, i.e. single-layer quantum neural network) based on it. The proposed QRBM has the following two salient features. (1) It is proved universal for implementing quantum computation tasks. (2) It can be efficiently implemented on the Noisy Intermediate-Scale Quantum (NISQ) devices. We successfully utilize the proposed QRBM to compute the wave functions for the notable cases of physical interest including the ground state as well as the Gibbs state (thermal state) of molecules on the superconducting quantum chip. The experimental results illustrate the proposed QRBM can compute the above wave functions with an acceptable error.

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“…In this section we look at the time evolution of Hamiltonians arising from fermionic many-body quantum systems. We use the spin Hamiltonians obtained in [14] by using the second quantization formalism of the fermionic system followed by a conversion to interacting spin models by applying the Jordan-Wigner, Bravyi-Kitaev, or parity encodings [11,23]. The resulting Hamiltonians are expressed as a weighted set of Paulis, as desired.…”

Section: Quantum Chemistrymentioning

confidence: 99%

Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters

Berg

Temme

2020

Quantum

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Many applications of practical interest rely on time evolution of Hamiltonians that are given by a sum of Pauli operators. Quantum circuits for exact time evolution of single Pauli operators are well known, and can be extended trivially to sums of commuting Paulis by concatenating the circuits of individual terms. In this paper we reduce the circuit complexity of Hamiltonian simulation by partitioning the Pauli operators into mutually commuting clusters and exponentiating the elements within each cluster after applying simultaneous diagonalization. We provide a practical algorithm for partitioning sets of Paulis into commuting subsets, and show that the proposed approach can help to significantly reduce both the number of CNOT operations and circuit depth for Hamiltonians arising in quantum chemistry. The algorithms for simultaneous diagonalization are also applicable in the context of stabilizer states; in particular we provide novel four- and five-stage representations, each containing only a single stage of conditional gates.

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Fermionic neural-network states for ab-initio electronic structure

Cited by 207 publications

References 43 publications

Retrospective on a decade of machine learning for chemical discovery

Retrospective on a decade of machine learning for chemical discovery

Quantum restricted Boltzmann machine is universal for quantum computation

Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters

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