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This paper investigates the feasibility of quantum simulations for quantum molecular dynamics, particularly focusing on reaction dynamics, by analyzing the conjugacy between quantum simulators and target molecular systems. It highlights the challenges posed by real-valued classical algorithms and the geometric phase resulting from the separation of degrees of freedom, which could hinder accurate simulations. The findings suggest that while quantum simulations may offer advantages, they also present significant theoretical obstacles that need to be addressed for practical implementation.
Quantum simulations could revolutionize our understanding of molecular reaction dynamics, but they face critical theoretical challenges that could limit their effectiveness.
In this work, we explore the implementation possibility of quantum simulation for quantum molecular dynamics, in particular for reaction dynamics, though several implementations have already reported through quantum-classical mixed simulations ({\it Acc. Chem. Res.} {\bf 54} (2021), 4229 and {\it J. Phys. Chem. Lett.} {\bf xx} (2026), XXXX). To analyze this aspect, we examine (1) the conjugacy relation between quantum simulator and the target molecular system, (2) the wave function correspondence in quantum algorithm and classical algorithm for multi-dimensional dynamics, (3) problems arisen from real-valued classical algorithms, and finally (4) geometric phase arisen from the separation among the degrees of freedom (DOFs). As is well known, the aforementioned first and second points play fundamental roles in quantum simulation of quantum many-body systems, and the third and fourth points are theoretical issues that might introduce problems in classical and quantum computing. In this work, we mainly focus on the third and fourth points by analysis of the first two points by reviewing previously reported quantum-classical mixed implementations of quantum simulation. We also consider gauge freedom in high-dimensional quantum molecular dynamics that has been introduced recently, and then discuss possibility of advantages and disadvantages of quantum simulation for molecular reaction dynamics.
