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Communications in Mathematical Physics

, Volume 284, Issue 2, pp 481–507 | Cite as

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

  • Sergey Bravyi
  • David DiVincenzo
  • Daniel Loss
Article

Abstract

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 H 0 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 H 0, 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.

Keywords

Ground State Energy Formal Power Series Small Eigenvalue Creation Operator Perturbative Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

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

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