Fault-Tolerant Quantum Computations of Vibrational Wave Functions

Area of Science:

• Quantum computing
• Computational chemistry
• Molecular vibrational spectroscopy

Background:

• Quantum computation offers potential advantages for molecular vibrational property calculations.
• Fault-tolerant quantum algorithms for these properties are underdeveloped.

Purpose of the Study:

• To develop and assess efficient quantum algorithms for encoding vibrational Hamiltonians.
• To explore various encoding strategies and computational techniques for improved performance.

Main Methods:

• Qubitization for vibrational Hamiltonian encoding.
• High-order tensor decomposition for Hamiltonian approximation.
• Investigation of different coordinate systems (rectilinear, polyspherical).
• Parallelization and grouping algorithms for computational efficiency.

Main Results:

• Benchmark computations on small and large molecules (up to 100+ vibrational modes).
• First resource estimates for qubitization of multimode vibrational Hamiltonians with high spectral resolution.
• Demonstrated reduction in T gate depth using tensor decomposition and operator parallelization.

Conclusions:

• Developed efficient quantum algorithms for molecular vibrational properties.
• Tensor decomposition and parallelization are key to reducing quantum computational cost.
• Paves the way for fault-tolerant quantum computations in computational chemistry.