Mapping multidimensional chemical dynamics problems to a family of hybrid quantum and classical computing environments

Despite ubiquitous applications of chemical dynamics simulations, the rendered computational cost grows exponentially with the degrees of freedom of a chemical system, limiting a classical computer to only specific chemical systems. This "curse of dimensionality" is further compounded by the quantum treatment of nuclear degrees of freedom which requires accurate time evolution of nuclear wavefunctions on precisely computed potential energy surfaces.

With 2ⁿ dimensional exponential Hilbert space for n qubit system, quantum computers are seen as having the potential to solve exponential scaling chemical dynamics problems. However, currently available NISQ computers still hinder progress due to low qubit counts and low-fidelity operations. One way to mitigate this issue is to use hybrid computing by pre-processing the problem on a classical computer before mapping it to a quantum computer.



In the same direction, our algorithm decomposes the multidimensional unitary operator and wavefunction into independent, parallel streams of one-dimensional propagators and wavefunctions using Tensor Networks such that an effective Hamiltonian for each dimension can be derived from it. Each one-dimensional system can be mapped to the spin-lattice quantum simulator, where the former determines the governing parameters needed to operate the quantum simulator. These effective one-dimensional subsystems can then be propagated simultaneously and efficiently on the quantum simulator.