2005/12/27 by Péter Jaksch, Jaksch, Peter
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.quant-ph/0512238
openalex publication_date 2005/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It has been shown that, starting from the state |0>, in the general case, an arbitrary quantum state |ψ> cannot be prepared with exponential precision in polynomial time. However, we show that for the important special case when |ψ> represents discrete values of some real, continuous function ψ(x), efficient preparation is possible by applying the eigenvalue estimation algorithm to a Hamiltonian which has ψ(x) as an eigenstate. We construct the required Hamiltonian explicitly and present an iterative algorithm for removing unwanted superpositions from the output state in order to reach |ψ> within exponential accuracy. The method works under very general conditions and can be used to provide the quantum simulation algorithm with very accurate and general starting states.