# Faster Quantum Chemistry Simulation on Fault-Tolerant Quantum Computers

 Title: Faster Quantum Chemistry Simulation on Fault-Tolerant Quantum Computers Author: Jones, N. Cody; Whitfield, James D.; McMahon, Peter L.; Yung, Man-Hong; Van Meter, Rodney; Aspuru-Guzik, Alan; Yamamoto, Yoshihisa Note: Order does not necessarily reflect citation order of authors. Citation: Jones, N. Cody, James D. Whitfield, Peter L. McMahon, Man-Hong Yung, Rodney Van Meter, Alán Aspuru-Guzik, and Yoshihisa Yamamoto. 2012. Faster quantum chemistry simulation on fault-tolerant quantum computers. New Journal of Physics 14(11): 115023. Full Text & Related Files: Jones_FasterQuantum.pdf (773.3Kb; PDF) Abstract: Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay–Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error $$\epsilon$$ , arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log $$\epsilon$$ ) or O(log log $$\epsilon$$  ); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride. Published Version: http://dx.doi.org/10.1088/1367-2630/14/11/115023 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10384783 Downloads of this work: