Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.Comment: 32 pages, 4 figure, to appear in The Journal of Chemical Physic

Fluctuation-Response Relations for Multi-Time Correlations

We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control term'' added as a modification to the master equation for statistical distributions. The proof of the relations is based upon a variational characterization of the generating functional of the time-correlations. The same fluctuation-response relations are preserved within moment-closures for the statistical dynamical system, when these are constructed via the variational Rayleigh-Ritz procedure. For the 2-time correlations of the moment-variables themselves, the fluctuation-response relation is equivalent to an ``Onsager regression hypothesis'' for the small fluctuations. For correlations of higher-order, there is a new effect in addition to such linear propagation of fluctuations present instantaneously: the dynamical generation of correlations by nonlinear interaction of fluctuations. In general, we discuss some physical and mathematical aspects of the {\it Ans\"{a}tze} required for an accurate calculation of the time correlations. We also comment briefly upon the computational use of these relations, which is well-suited for automatic differentiation tools. An example will be given of a simple closure for turbulent energy decay, which illustrates the numerical application of the relations.Comment: 28 pages, 1 figure, submitted to Phys. Rev.

Basis set generation and optimization in the NISQ era with Quiqbox.jl

In the noisy intermediate-scale quantum era, ab initio computation of the electronic structure problem has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. The single-particle basis set plays a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of the single-particle basis set, we propose a framework for more customizable basis set generation and basis set optimization. This framework allows configurations of composite Gaussian-type basis functions to go beyond typical Gaussian-type basis set frameworks such as the atomic orbitals and floating basis sets. Such basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source electronic structure package named ``Quiqbox'' in the Julia programming language. Both the Hartree--Fock procedure and Gaussian-based electronic integral computations are implemented in this package. We compare Quiqbox with the basis set optimization package DiffiQult and find faster convergence of the basis set optimization with lower run time. We also demonstrate the additional customizability Quiqbox brings for more systematic basis set research with an example of constructing and optimizing delocalized orbitals.Comment: 15 pages, 7 figures, 5 tables, 1 listin

Instead of Rewriting Foreign Code for Machine Learning, Automatically Synthesize Fast Gradients

Applying differentiable programming techniques and machine learning algorithms to foreign programs requires developers to either rewrite their code in a machine learning framework, or otherwise provide derivatives of the foreign code. This paper presents Enzyme, a high-performance automatic differentiation (AD) compiler plugin for the LLVM compiler framework capable of synthesizing gradients of statically analyzable programs expressed in the LLVM intermediate representation (IR). Enzyme synthesizes gradients for programs written in any language whose compiler targets LLVM IR including C, C++, Fortran, Julia, Rust, Swift, MLIR, etc., thereby providing native AD capabilities in these languages. Unlike traditional source-to-source and operator-overloading tools, Enzyme performs AD on optimized IR. On a machine-learning focused benchmark suite including Microsoft's ADBench, AD on optimized IR achieves a geometric mean speedup of 4.5x over AD on IR before optimization allowing Enzyme to achieve state-of-the-art performance. Packaging Enzyme for PyTorch and TensorFlow provides convenient access to gradients of foreign code with state-of-the art performance, enabling foreign code to be directly incorporated into existing machine learning workflows.Comment: To be published in NeurIPS 202

General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules

A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH$_3$). The method extends the general variational approach TROVE by adding the extra term in the Hamiltonian that describes the nuclear quadrupole coupling, with no inherent limitation on the number of quadrupolar nuclei in a molecule. We applied the new approach to compute the nitrogen-nuclear-quadrupole hyperfine structure in the rovibrational spectrum of NH$_3$. These results agree very well with recent experimental spectroscopic data for the pure rotational transitions in the ground vibrational and $\nu_2$ states, and the rovibrational transitions in the $\nu_1$, $\nu_3$, $2\nu_4$, and $\nu_1+\nu_3$ bands. The computed hyperfine-resolved rovibrational spectrum of ammonia will be beneficial for the assignment of experimental rovibrational spectra, further detection of ammonia in interstellar space, and studies of the proton-to-electron mass variation