Randomized Algorithms for Hamiltonian Simulation

  • Chi ZhangEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)


We consider randomized algorithms for simulating the evolution of a Hamiltonian \(H ={ \sum \nolimits }_{j=1}^{m}{H}_{j}\) for time t. The evolution is simulated by a product of exponentials of H j in a random sequence, and random evolution times. Hence the final state of the system is approximated by a mixed quantum state. First we provide a scheme to bound the error of the final quantum state in a randomized algorithm. Then we obtain randomized algorithms which have the same efficiency as certain deterministic algorithms but which are simpler to implement.



We are grateful to Anargyros Papageorgiou, Joseph F. Traub, Henryk Wozniakowski, Columbia University and Zhengfeng Ji, Perimeter Institute for Theoretical Physics, for their very helpful discussions and comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceColumbia UniversityNew YorkUSA

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