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The computational cost of exact methods for quantum simulation usingclassical computers grows exponentially with system size. As a consequence,these techniques can only be applied to small systems. By contrast, wedemonstrate that quantum computers could exactly simulate chemical reactions inpolynomial time. Our algorithm uses the split-operator approach and explicitlysimulates all electron-nuclear and inter-electronic interactions in quadratictime. Surprisingly, this treatment is not only more accurate than theBorn-Oppenheimer approximation, but faster and more efficient as well, for allreactions with more than about four atoms. This is the case even though theentire electronic wavefunction is propagated on a grid with appropriately shorttimesteps. Although the preparation and measurement of arbitrary states on aquantum computer is inefficient, here we demonstrate how to prepare states ofchemical interest efficiently. We also show how to efficiently obtainchemically relevant observables, such as state-to-state transitionprobabilities and thermal reaction rates. Quantum computers using thesetechniques could outperform current classical computers with one hundredqubits.

Polynomial-time quantum algorithm for the simulation of chemical dynamics