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Molecular Quantum Dynamics: A Quantum Computing Perspective.

Pauline J Ollitrault1, Alexander Miessen1, Ivano Tavernelli1

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Quantum algorithms offer a promising path to overcome the computational cost of simulating molecular dynamics, especially for complex non-adiabatic processes. These novel algorithms demonstrate favorable scaling compared to classical methods, potentially enabling more accurate simulations in computational chemistry.

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Area of Science:

  • Computational Chemistry
  • Quantum Dynamics
  • Algorithm Development

Background:

  • Simulating molecular dynamics (MD) under a comprehensive quantum framework is computationally intensive due to the exponential scaling of solving the time-dependent Schrödinger equation (TDSE).
  • The Born-Oppenheimer (BO) approximation simplifies simulations by decoupling electronic and nuclear motions, but breaks down in non-adiabatic dynamics, necessitating solutions that include electron-nuclear couplings.
  • Existing methods like the multiconfigurational time-dependent Hartree (MCTDH) struggle with exponential scaling in nuclear degrees of freedom (DOFs) and finding universal variational forms.

Purpose of the Study:

  • To present novel quantum computational algorithms designed to mitigate the exponential scaling challenges in simulating many-body quantum dynamics.
  • To explore the application of these quantum algorithms for both adiabatic and non-adiabatic quantum dynamics, including efficient calculation of Born-Oppenheimer potential energy surfaces (PESs).
  • To analyze the scaling properties and potential quantum advantage of different quantum algorithms for molecular quantum dynamics simulations.

Main Methods:

  • Development and application of quantum algorithms for adiabatic and non-adiabatic quantum dynamics.
  • Efficient computation of Born-Oppenheimer potential energy surfaces (PESs).
  • Time-evolution of a model system with two coupled PESs using quantum algorithms in first and second quantization, including a variational quantum algorithm (VQA) and Trotter-type evolution.

Main Results:

  • A quantum algorithm for wavepacket evolution in first quantization demonstrates potential quantum advantage by mapping spatial grids to logarithmically many qubits.
  • In second quantization, both VQA and Trotter-type evolution algorithms show favorable scaling properties compared to classical approaches for time-evolution.
  • The study highlights the potential of quantum algorithms for molecular quantum dynamics but notes that fault-tolerant quantum computers may be required for a clear demonstration of quantum advantage.

Conclusions:

  • Novel quantum algorithms show promise in alleviating the computational burden of simulating molecular quantum dynamics.
  • These algorithms exhibit favorable scaling compared to classical methods, particularly for non-adiabatic processes.
  • Further research and implementation on fault-tolerant quantum computers are needed to fully realize the potential of quantum advantage in this field.