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Towards Analyzing Formic Acid Using Classical and Quantum Methods

Omer Gurevich, Tal Mor, Ido Ram

Abstract

Catalytic carbon fixation to formic acid is important for studying the reduction of carbon footprint and the emergence of life. Can discrete quantum exhaustive search merged with other methods help reduce the carbon footprint? We suggest merging quantum, quantum inspired, and classical tools for a better simulation of various relevant processes. Quantum tools are often used for analyzing the electronic structure of molecules, sometimes because this problem is not scalable (in the number of orbitals) on classical computers while it is potentially approximately scalable on (future) quantum computers. It is potentially even solvable in the near future using variational quantum eigensolvers (VQE) yet a major obstacle to such analysis is the appearance of barren plateaus in the Hilbert space describing the problem. Here we make use of the basic (standard) tools while also including a novel one -- the discrete quantum exhaustive search, which relies on mutually unbiased bases, for analyzing the simplest non-catalytic process involving carbon dioxide, hydrogen and formic acid.

Towards Analyzing Formic Acid Using Classical and Quantum Methods

Abstract

Catalytic carbon fixation to formic acid is important for studying the reduction of carbon footprint and the emergence of life. Can discrete quantum exhaustive search merged with other methods help reduce the carbon footprint? We suggest merging quantum, quantum inspired, and classical tools for a better simulation of various relevant processes. Quantum tools are often used for analyzing the electronic structure of molecules, sometimes because this problem is not scalable (in the number of orbitals) on classical computers while it is potentially approximately scalable on (future) quantum computers. It is potentially even solvable in the near future using variational quantum eigensolvers (VQE) yet a major obstacle to such analysis is the appearance of barren plateaus in the Hilbert space describing the problem. Here we make use of the basic (standard) tools while also including a novel one -- the discrete quantum exhaustive search, which relies on mutually unbiased bases, for analyzing the simplest non-catalytic process involving carbon dioxide, hydrogen and formic acid.

Paper Structure

This paper contains 43 sections, 15 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Carbon fixation and climate change
  3. Impact on humanity
  4. Formic acid and Origin of Life
  5. Review of the Algorithms Used
  6. Background
  7. Electronic Structure Problem
  8. Potential Energy Surface
  9. Reaction Coordinate
  10. Transition States
  11. Classical Methods
  12. Single-Point Energy Calculation
  13. Potential Energy Surface Calculation
  14. Transition State Calculation - NEB Method
  15. Intrinsic Reaction Coordinate
  16. ...and 28 more sections

Figures (14)

  • Figure 1: Main prebiotic building blocks that can be synthesized from formamide under plausible prebiotic conditions ref:saladino2012genetics, ref:saladino2015meteorite.
  • Figure 2: 2d PES of co-linear dynamics of three hydrogen atoms.
  • Figure 3: 2d PES of co-linear dynamics of two oxygens around a carbon atom.
  • Figure 4: 2d PES of water molecule.
  • Figure 5: The Energy Error spread in 6 qubits EfficientSU2 (left; in log-scale) and UCCSD (right) in VQE trials (Blue) and MUB trials (Red).
  • ...and 9 more figures