Trotter Simulation of Vibrational Hamiltonians on a Quantum Computer.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Molecular Dynamics

Background:

• Simulating molecular vibrations is key for understanding molecular structure and applications like vibrational spectroscopy.
• Quantum algorithms show promise for vibrational dynamics but are less developed than electronic structure simulations.
• Classical simulations of molecular vibrations are computationally intensive.

Purpose of the Study:

• To develop and compare efficient quantum algorithms for simulating molecular vibrational dynamics.
• To introduce optimized fragmentation schemes and error estimation for quantum vibrational simulations.
• To demonstrate the feasibility of simulating vibrational spectra using quantum computers.

Main Methods:

• Detailed description of three forms of the vibrational Hamiltonian: canonical bosonic quantization, real space, and Christiansen second-quantized.
• Development of fragmentation schemes leveraging Lie algebraic properties for Trotter product formulas.
• Perturbative approach for Trotter error estimation to calculate T gate costs.

Main Results:

• An optimized quantum framework for simulating vibrational dynamics is presented.
• For methane (CH4) with 9 modes, 1.8 ps of dynamics can be simulated with 36 qubits and ~3x10^8 T gates.
• This represents an order-of-magnitude speedup over current state-of-the-art quantum algorithms.

Conclusions:

• The developed framework offers a unified and highly optimized approach for quantum simulations of vibrational dynamics.
• Simulating vibrational spectra demonstrates the fidelity of the proposed quantum algorithms.
• Quantum computing is positioned as an attractive platform for molecular vibrational dynamics simulations.