Communications in Mathematical Physics

, Volume 284, Issue 2, pp 481–507

Polynomial-Time Algorithm for Simulation of Weakly Interacting Quantum Spin Systems


DOI: 10.1007/s00220-008-0574-6

Cite this article as:
Bravyi, S., DiVincenzo, D. & Loss, D. Commun. Math. Phys. (2008) 284: 481. doi:10.1007/s00220-008-0574-6


We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial in n and δ−1, where n is the number of qubits, and δ is the required precision. Specifically, we consider Hamiltonians of the form \({H=H_0+ \epsilon V}\) , where H0 describes non-interacting qubits, V is a perturbation that involves arbitrary two-qubit interactions on a graph of bounded degree, and \({\epsilon}\) is a small parameter. The algorithm works if \({|\epsilon|}\) is below a certain threshold value \({\epsilon_0}\) that depends only upon the spectral gap of H0, the maximal degree of the graph, and the maximal norm of the two-qubit interactions. The main technical ingredient of the algorithm is a generalized Kirkwood-Thomas ansatz for the ground state. The parameters of the ansatz are computed using perturbative expansions in powers of \({\epsilon}\) . Our algorithm is closely related to the coupled cluster method used in quantum chemistry.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA
  2. 2.Department of PhysicsUniversity of BaselBaselSwitzerland