Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation

Details Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation

2003-08-04

arxiv.org/abs/quant-ph/0308016v1

Physics

Quantum Physics

4 pages

Scientific paper

10.1103/PhysRevLett.91.257902

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quantum mechanically, an approximation of the same eigenvector on a fine grid. We use this approximation as the initial state for the eigenvalue estimation algorithm, and show the relationship between its success probability and the size of the coarse grid.

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