Accurate Sampling with Noisy Forces from Approximate Computing

Abstract

In scientific computing, the acceleration of atomistic computer simulations by means of custom hardware is finding ever growing application. A major limitation, however, is that the high efficiency in terms of performance and low power consumption entails the massive usage of low-precision computing units. Here, based on the approximate computing paradigm, we present an algorithmic method to rigorously compensate for numerical inaccuracies due to low-accuracy arithmetic operations, yet still obtaining exact expectation values using a properly modified Langevin-type equation.

Towards Electronic Structure-Based Ab-Initio Molecular Dynamics Simulations with Hundreds of Millions of Atoms

“…All quantities depend on the position of the atoms R 1 , ..., R n . In previous works we have demonstrated that in the present context Ξ i can be assumed to be nearly unbiased [14], [18], [19], thus fulfilling the so-called fluctuation-dissipation theorem…”

“…We demonstrate that by leveraging the approximate computing (AC) paradigm [16], [17], the usage of mixed-and low-precision numerics can be rigorously compensated by an appropriately modified Langevin-type equation. The noise within the nuclear forces can be assumed as white, thus facilitating the exact computation of ensemble-averaged expectation values [14], [18], [19]. One possible route is the linear-scaling sign-method [20], which only relies on large sparse matrix-matrix multiplies.…”

“…Although the fluctuation-dissipation theorem has been used in the context of MD simulations for some time, we apply it here to facilitate to usage of noisy forces F N i from approximate electronic structure calculations in lower arithmetic precision and still obtain accurate thermodynamic quantities [19].…”

Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers

“…The variational formulation based on RDMFT makes the proposed algorithm very suitable for ab-initio molecular dynamics calculations because the forces can be evaluated in a straightforward way from already available quantities such as the one-and two-particle reduced density matrix [52]. Noise in the nuclear forces stemming from the noise of the quantum computer can be compensated for in ab-initio molecular dynamics simulations in the spirit of approximate computing [53], where the desired thermodynamic expectation values can nevertheless be accurately obtained by devising a properly modified Langevin equation [54,55]. The investigation of the representability of fermionic quantum states on noisy gate-based quantum computers, the optimization of the measurement programs as well as the integration with molecular dynamics programs like CP2K [56] were permitted.…”

Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics

“…This article is building on the implementation described in Schade et al (2022), but since we are focusing on improvements to increase the sustained peak performance, aspects like the compensation of noise from numerical approximations with an appropriately modified Langevin-type equation to obtain accurate thermodynamical expectation values are not touched here, but have been discussed in previous work (Richters and Kühne 2014; Rengaraj et al, 2020). Instead, Section II summarizes the tackled problem, whereas Section III puts the achievement in relation to the performance of related large-scale electronic structure–based structure relaxations or AIMD simulations.…”