Polynomialtime quantum algorithm for the simulation of chemical dynamics
Abstract
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the splitoperator approach and explicitly simulates all electronnuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the BornOppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as statetostate transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 December 2008
 DOI:
 10.1073/pnas.0808245105
 arXiv:
 arXiv:0801.2986
 Bibcode:
 2008PNAS..10518681K
 Keywords:

 Physical Sciences:Chemistry;
 Quantum Physics
 EPrint:
 9 pages, 3 figures. Updated version as appears in PNAS